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The characterization of the covariance function of the solution process to a stochastic partial differential equation is considered in the parabolic case with multiplicative Lévy noise of affine type. For the second moment of the mild solution, a well-posed deterministic space-time variational problem posed on project... |
We consider the 2D stochastic Ising model evolving according to the Glauber dynamics at zero temperature. We compute the initial drift for droplets which are suitable approximations of smooth domains. |
We study existence and regularity of the density for the solution $u(t,x)$ (with fixed $t > 0$ and $x \in D$) of the heat equation in a bounded domain $D \subset \mathbb R^d$ driven by a stochastic inhomogeneous Neumann boundary condition with stochastic term. The stochastic perturbation is given by a fractional Br... |
Consider a supercritical superdiffusion (X_t) on a domain D subset R^d with branching mechanism <br>-\beta(x) z+\alpha(x) z^2 + int_{(0,infty)} (e^{-yz}-1+yz) Pi(x,dy). <br>The skeleton decomposition provides a pathwise description of the process in terms of immigration along a branching particle diffusion. |
We introduce and study an alternative form of the chaotic expansion for counting processes using the Poisson imbedding representation; we name this alternative form \textit{pseudo-chaotic expansion}. As an application, we prove that the coefficients of this pseudo-chaotic expansion for any linear Hawkes process are ob... |
We prove Griffiths inequalities for the $O(N)$-spin model with inhomogeneous coupling constants and external magnetic field for any $N\geq 2$. This is achieved by using a representation of $O(N)$-spins in terms of random paths that reduces to the random current representation of the Ising model for $N=1$ and an identi... |
In this article we study the asymptotic behaviour of the realized quadratic variation of a process $\int_{0}^{t}u_{s}dG^{H}_{s}$, where $u$ is a $\beta$-Hölder continuous process with $\beta >1-H$ and $G^H$ is a self-similar Gaussian process with parameters $H\in(0,3/4)$. We prove almost sure convergence uniformly ... |
We propose a new approach to studying classical solutions of the Bellman equation and Master equation for mean field type control problems, using a novel form of the "lifting" idea introduced by P. -L. |
The two-time distribution gives the limiting joint distribution of the heights at two different times of a local 1D random growth model in the curved geometry. This distribution has been computed in a specific model but is expected to be universal in the KPZ universality class. |
In this study, we investigate $N$-player stochastic differential games with regime switching, where the player dynamics are modulated by a finite-state Markov chain. We analyze the associated Nash system, which consists of a system of coupled nonlinear partial differential equations, and establish the existence and un... |
We investigate the random continuous trees called Lévy trees, which are obtained as scaling limits of discrete Galton-Watson trees. We give a mathematically precise definition of these random trees as random variables taking values in the set of equivalence classes of compact rooted R-trees, which is equipped with the... |
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. |
The Goodman-Nguyen relation is a partial order generalising the implication (inclusion) relation to conditional events. As such, with precise probabilities it both induces an agreeing probability ordering and is a key tool in a certain common extension problem. |
In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in R^d is joined by an edge to its nearest-neighbour amongst those points that precede it in the sequence. We study the large-sample asymptotic behaviour of the total power-weighted length of the ONG on uniform random poin... |
A stochastic forest model of young and old age class trees is studied. First, we prove existence, uniqueness and boundedness of global nonnegative solutions. |
We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company b... |
We consider a 2D stochastic wave equation driven by a Gaussian noise, which is temporally white and spatially colored described by the Riesz kernel. Our first main result is the functional central limit theorem for the spatial average of the solution. |
We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with the dimension, and the perturbation matrix is drawn from one of several different... |
The Itô formula, also known as the change-of-variables formula, is a cornerstone of Itô stochastic calculus. Over time, this formula has been extended to apply to random processes for which classical calculus is insufficient. |
The $i$-dimensional plaquette random-cluster model on a finite cubical complex is the random complex of $i$-plaquettes with each configuration having probability proportional to $$p^{\text{# of plaquettes}}(1-p)^{\text{# of complementary plaquettes}}q^{\mathbf{ b}_{i-1}},$$ where $q\geq 1$ is a real parameter and $\mat... |
In this paper, Wang's log-Harnack inequality and exponential ergodicity are derived for two types of distribution dependent SDEs: one is the CKLS model, where the diffusion coefficient is a power function of order $\theta$ with $\theta\in[\frac{1}{2},1)$; the other one is Vasicek model, where the diffusion coeffici... |
We consider the simple random walk on the $N$-dimensional integer lattice from the perspective of evaluating asymptotically the duration of play in the multidimensional gambler\apost s ruin problem. We show that, under suitable rescalings, all $p$-moments of exit-times from balls in the $L$-infinity metric, and all $p... |
We consider an infinite system of particles in one dimension, each particle performs independant Sinai's random walk in random environment. Considering an instant $t$, large enough, we prove a result in probability showing that the particles are trapped in the neighborhood of well defined points of the lattice dep... |
We study a planar random motion $\big(X(t),\,Y(t)\big)$ with orthogonal directions, where the direction switches are governed by a homogeneous Poisson process. At each Poisson event, the moving particle turns clockwise or counterclockwise according to a rule which depends on the current direction. |
We consider the supermarket model in the usual Markovian setting where jobs arrive at rate $n \lambda_n$ for some $\lambda_n > 0$, with $n$ parallel servers each processing jobs in its queue at rate 1. An arriving job joins the shortest among $d_n \le n$ randomly selected service queues. |
This paper studies the asymptotic growth and decay properties of solutions of the stochastic pantograph equation with multiplicative noise. We give sufficient conditions on the parameters for solutions to grow at a polynomial rate in $p$-th mean and in the almost sure sense. |
We present remarkably simple proofs of Burkholder-Davis-Gundy inequalities for stochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces driven by Lévy-type processes. Exponential estimates for stochastic convolutions are obtained and two versions of Itô's formula in Banach spaces ... |
In this paper, we study the backward stochastic differential equations driven by G-Brownian motion with double mean reflections, which means that the constraints are made on the law of the solution. Making full use of the backward Skorokhod problem with two nonlinear reflecting boundaries and the fixed-point theory, t... |
We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are their applications to multiple recurrence for stochastic processes and dynamic... |
The stationary distribution of a continuous-time Markov chain generally arises from a complicated global balance of probability fluxes. Nevertheless, empirical evidence shows that the effective potential, defined as the negative logarithm of the stationary distribution, is often highly correlated with a simple local p... |
We consider a stochastic Cahn-Hilliard partial differential equation driven by a space-time white noise. We prove the Large Deviations Principle (LDP) for the law of the solutions in the Hölder norm. |
First order stochastic dominance and monotone likelihood ratio are two partial orders on the $n$-probability simplex that play an important role in the establishment of structural results for MDPs and POMDPs. We study the strength of those partial orders in terms of how likely it is for two random points on the $n$-pr... |
We compute the eigenvalue fluctuations of uniformly distributed random biregular bipartite graphs with fixed and growing degrees for a large class of analytic functions. As a key step in the proof, we obtain a total variation distance bound for the Poisson approximation of the number of cycles and cyclically non-backt... |
Neuhauser [Probab. Theory Related Fields 91 (1992) 467--506] considered the two-type contact process and showed that on $\mathbb{Z}^2$ coexistence is not possible if the death rates are equal and the particles use the same dispersal neighborhood. Here, we show that it is possible for a species with a long-, but finite... |
This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. |
In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a stochastic control problem for an evolution system in an Hilbert space. |
We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N-by-N box, with boundary conditions which are ``plus'' except for small regions at the corners which are either free or ``minus. '' The spectral gap decreases exponentially in the size of the corner re... |
We investigate the hydrodynamical behavior of a system of random walks with zero-range interactions moving in a common `Sinai-type' random environment on a one dimensional torus. The hydrodynamic equation found is a quasilinear SPDE with a `rough' random drift term coming from a scaling of the random environme... |
The $L^p$ boundedness on vertical Littlewood--Paley square functions for heat flows on $\textup{RCD}(K,\infty)$ spaces with $K\in\mathbb{R}$ is proved. With regards to the proof, for $1<p\leq 2$, Stein's analytical method is applied, while for $2<p<\infty$, the probabilistic approach in the sense of Bañuel... |
The main result in this paper is a variational formula for the exit rate from a bounded domain for a diffusion process in terms of the stationary law of the diffusion constrained to remain in this domain forever. Related results on the geometric ergodicity of the controlled Q-process are also presented. |
We prove that with high probability, d+1 random Bernoulli polynomials in d variables of degree n (n goes to infinity) do not possess a common root. |
In this paper we specify some facts about the sequence of polynomials associated to a \CSK family and we prove that quadratic variance function is characterized by the property of orthogonality of these polynomials. |
In the Wiener disorder problem, the drift of a Wiener process changes suddenly at some unknown and unobservable disorder time. The objective is to detect this change as quickly as possible after it happens. |
We consider a class of linear Volterra transforms of Brownian motion associated to a sequence of Müntz Gaussian spaces and determine explicitly their kernels; some interesting links with Müntz-Legendre polynomials are provided. This gives new explicit examples of progressive Gaussian enlargement of the Brownian filtra... |
The work concerns invariant measures for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the exponential ergodicity of these equations. |
In this paper we develop a model of stochastic gene expression, which is an extension of the model investigated in the paper [T. Lipniacki, P. Paszek, A. Marciniak-Czochra, A.R. Brasier, M. Kimmel, Transcriptional stochasticity in gene expression, J. Theor. Biol. 238 (2006) 348-367]. In our model, stochastic effects s... |
In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. |
We study an evolution problem in the space of continuous loops in three-dimensional Euclidean space modelled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting from Hölder regular loops with index greater than 1/3. |
We derive general sufficient conditions for the existence of Riemann-Stieltjes integrals $\int_a^b Yd X$. Our results extend the classical conditions of <a href="http://L.C.Young" rel="external noopener nofollow" class="link-external link-http">this http URL</a> and improve some recent results that deal with integrals... |
In this paper, inspired by the fractional Brownian sheet of Riemann-Liouville type, we introduce the operator fractional Brownian sheet of Riemman-Liouville type, and study some properties of it. We also present an approximation in law to it based on the martingale differences. |
Under suitable assumptions on $\beta:\mathbb{R}\! \to\! |
In this article we prove several important properties of 2^{k-p} minimum aberration (MA) designs with k>2, where n=2^{k-p} is the number of runs. We develop a simple method to build MA designs of resolution III. |
Suppose we are given finitely generated groups $\Gamma_1,...,\Gamma_m$ equipped with irreducible random walks. Thereby we assume that the expansions of the corresponding Green functions at their radii of convergence contain only logarithmic or algebraic terms as singular terms up to sufficiently large order (except fo... |
In this manuscript, we consider the Langevin dynamics on $\mathbb{R}^d$ with an overdamped vector field and driven by multiplicative Brownian noise of small amplitude $\sqrt{\epsilon}$, $\epsilon>0$. Under suitable assumptions on the vector field and the diffusion coefficient, it is well-known that it possesses a u... |
We show that the stationary density fluctuations of exclusion processes with long jumps, whose rates are of the form $c^\pm |y-x|^{-(1+\alpha)}$ where $c\pm$ depends on the sign of $y-x$, are given by a fractional Ornstein-Uhlenbeck process for $\alpha \in (0,\frac{3}{2})$. When $\alpha =\frac{3}{2}$ we show that the ... |
An infinite buffer batch service vacation queue has been studied where service rate of the batch is dependent on the size of the batch and vacation rate is dependent on the queue size at vacation initiation epoch. The arrivals follow the Markovian arrival process (MAP). |
Suppose that $X=\{X_t, t\ge 0; \mathbb{P}_{\mu}\}$ is a supercritical superprocess in a locally compact separable metric space $E$. Let $\phi_0$ be a positive <br>eigenfunction corresponding to the first eigenvalue $\lambda_0$ of the generator of the mean semigroup of $X$. |
We consider systems of damped wave equations with a state-dependent damping coefficient and perturbed by a Gaussian multiplicative noise. Initially, we investigate their well-posedness, under quite general conditions on the friction. |
We obtain dimension-free concentration inequalities for $\ell^p$-norms, $p\geq2$, of infinitely divisible random vectors with independent coordinates and finite exponential moments. Besides such norms, the methods and results extend to some other classes of Lipschitz functions. |
In this paper, we establish an exponential inequality for U-statistics of i.i.d. data, varying kernel and taking values in a separable Hilbert space. The bound are expressed as a sum of an exponential term plus an other one involving the tail of a sum of squared norms. |
The well known bunkbed conjecture about percolation on finite graphs is now resolved; Gladkov, Pak and Zimin, building upon work of Hollom, have constructed a counterexample. We revisit this conjecture and study it in the broader context of the class of random cluster measures. |
In this paper, we study the qualitative behaviour of approximation schemes for Backward Stochastic Differential Equations (BSDEs) by introducing a new notion of numerical stability. For the Euler scheme, we provide sufficient conditions in the one-dimensional and multidimensional case to guarantee the numerical stabil... |
For a class of (non-symmetric) diffusion processes on a length space, which in particular include the (reflecting) diffusion processes on a connected compact Riemannian manifold, the exact convergence rate is derived for $({\mathbb E} [{\mathbb W}_p^q(\mu_T,\mu)])^{\frac{1}{q}} (T \to \infty)$ uniformly in $(p,q)\in [1... |
Much work in the study of large deviations for random graph models is focused on the dense regime where the theory of graphons has emerged as a principal tool. These tools do not give a good approach to large deviation problems for random graph models in the sparse regime. |
A p.c.f. fractal with a regular harmonic structure admits an associated Dirichlet form, which is itself associated with a Laplacian. This Laplacian enables us to give an analogue of the damped stochastic wave equation on the fractal. |
For a $d$-dimensional stochastic process $(S_n)_{n=0}^N$ we obtain criteria for the existence of an equivalent martingale measure, whose density $z$, up to a normalizing constant, is bounded from below by a given random variable $f$. We consider the case of one-period model (N=1) under the assumptions $S\in L^p$; $f,z... |
We prove the existence of scaling limits for the projection on the backbone of the random walks on the Incipient Infinite Cluster and the Invasion Percolation Cluster on a regular tree. We treat these projected random walks as randomly trapped random walks (as defined in [BCČR15]) and thus describe these scaling limit... |
Let $Q_n$ denote a random symmetric $n$ by $n$ matrix, whose upper diagonal entries are i.i.d. Bernoulli random variables (which take values 0 and 1 with probability 1/2). We prove that $Q_n$ is non-singular with probability $1-O(n^{-1/8+\delta})$ for any fixed $\delta > 0$. |
By using the Skorohod equation we derive an iteration procedure which allows us to solve a class of reflected backward stochastic differential equations with non-linear resistance induced by the reflected local time. In particular, we present a new method to study the reflected BSDE proposed first by El Karoui et al. |
In this paper, we describe an IDE called CAPS (Calculational Assistant for Programming from Specifications) for the interactive, calculational derivation of imperative programs. In building CAPS, our aim has been to make the IDE accessible to non-experts while retaining the overall flavor of the pen-and-paper calculat... |
Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices, which use different gate sets, and can miss optimizations that are hard to find m... |
In this paper I introduce a mechanism to derive program transforma- tions from order-preserving transformations of vector types. The purpose of this work is to allow automatic generation of correct-by-construction instances of programs in a streaming data processing paradigm suitable for FPGA processing. |
Python's typing system has evolved pragmatically into a powerful but theoretically fragmented system, with scattered specifications. This paper proposes a formalization to address this fragmentation. |
In December 2023, security agencies from five countries in North America, Europe, and the south Pacific produced a document encouraging senior executives in all software producing organizations to take responsibility for and oversight of the security of the software their organizations produce. In February 2024, the W... |
We define a domain-specific language (DSL) to inductively assemble flow networks from small networks or modules to produce arbitrarily large ones, with interchangeable functionally-equivalent parts. Our small networks or modules are "small" only as the building blocks in this inductive definition (there is no ... |
We reduce JavaScript to a core calculus structured as a small-step operational semantics. We present several peculiarities of the language and show that our calculus models them. |
Fold functions are a general mechanism for computing over recursive data structures. First-order folds compute results bottom-up. |
We present an implementation of an interpreter LRPi for the call-by-need calculus LRP, based on a variant of Sestoft's abstract machine Mark 1, extended with an eager garbage collector. It is used as a tool for exact space usage analyses as a support for our investigations into space improvements of call-by-need c... |
Programming models for distributed and heterogeneous machines are rapidly growing in popularity to meet the demands of modern workloads. Task and actor models are common choices that offer different trade-offs between development productivity and achieved performance. |
Modern JavaScript includes the SharedArrayBuffer feature, which provides access to true shared memory concurrency. SharedArrayBuffers are simple linear buffers of bytes, and the JavaScript specification defines an axiomatic relaxed memory model to describe their behaviour. |
Probabilistic Programming Languages (PPLs) allow users to encode statistical inference problems and automatically apply an inference algorithm to solve them. Popular inference algorithms for PPLs, such as sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC), are built around checkpoints -- relevant events ... |
Context-free language (CFL) reachability is a standard approach in static analyses, where the analysis question is phrased as a language reachability problem on a graph $G$ wrt a CFL L. While CFLs lack the expressiveness needed for high precision, common formalisms for context-sensitive languages are such that the corr... |
Reductions combine collections of inputs with an associative (and here, also commutative) operator to produce collections of outputs. When the same value contributes to multiple outputs, there is an opportunity to reuse partial results, enabling reduction simplification. |
High-level synthesis (HLS) is a process that automatically translates a software program in a high-level language into a low-level hardware description. However, the hardware designs produced by HLS tools still suffer from a significant performance gap compared to manual implementations. |
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although satisfiable systems of higher-order clauses do not generally have least models, t... |
There is a growing interest in running legal contracts on digital systems, at the same time, it is important to understand to what extent software contracts may capture legal content. We then undertake a foundational study of legal contracts and we distill four main features: agreement, permissions, violations and obl... |
Region-based memory management (RBMM) is a form of compile time memory management, well-known from the functional programming world. In this paper we describe our work on implementing RBMM for the logic programming language Mercury. |
Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. |
The multiway rendezvous introduced in Theoretical CSP is a powerful paradigm to achieve synchronization and communication among a group of (possibly more than two) processes. We illustrate the advantages of this paradigm on the production cell benchmark, a model of a real metal processing plant, for which we propose a... |
We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially bounded as a function of the input; and similarly for the running time. |
Suenaga and Hasuo introduced a nonstandard programming language ${\bf While}^{\bf dt}$ which models hybrid systems. We demonstrate why ${\bf While}^{\bf dt}$ is not suitable for modeling actual computations. |
Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving that they generate samples from the correct distribution - is crucial to the use... |
We introduce a type system for the Quipper language designed to derive upper bounds on the size of the circuits produced by the typed program. This size can be measured according to various metrics, including width, depth and gate count, but also variations thereof obtained by considering only some wire types or some ... |
A new theory of programming is proposed. The theory consists of OE (Operation Expression), SP (Semantic Predicate) and A (Axiom), abbreviated as OESPA. |
Design of an efficient thread-safe concurrent data structure is a balancing act between its implementation complexity and performance. Lock-based concurrent data structures, which are relatively easy to derive from their sequential counterparts and to prove thread-safe, suffer from poor throughput under even light mul... |
The Web of Linked Data is the cumulation of over a decade of work by the Web standards community in their effort to make data more Web-like. We provide an introduction to the Web of Linked Data from the perspective of a Web developer that would like to build an application using Linked Data. |
Provenance is an increasing concern due to the ongoing revolution in sharing and processing scientific data on the Web and in other computer systems. It is proposed that many computer systems will need to become provenance-aware in order to provide satisfactory accountability, reproducibility, and trust for scientific... |
In this article, we introduce an instruction set architecture (ISA) for processing-in-memory (PIM) based deep neural network (DNN) accelerators. The proposed ISA is for DNN inference on PIM-based architectures. |
We present a new role system for specifying changing referencing relationships of heap objects. The role of an object depends, in large part, on its aliasing relationships with other objects, with the role of each object changing as its aliasing relationships change. |
Computing precise (fully flow-sensitive and context-sensitive) and exhaustive points-to information is computationally expensive. Many practical tools approximate the points-to information trading precision for efficiency. |
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