| { | |
| "system_id": "stochastic_ou", | |
| "name": "Ornstein–Uhlenbeck process", | |
| "category": "stochastic", | |
| "equations": "dx_t = -θ (x_t - μ) dt + σ dW_t", | |
| "parameters": { | |
| "theta": 1.0, | |
| "mu": 0.0, | |
| "sigma": 0.5 | |
| }, | |
| "description_simple": "A stochastic process with mean-reverting dynamics driven by Gaussian noise.", | |
| "description_complex": "A continuous-time stochastic differential equation describing a mean-reverting Gaussian process driven by Brownian motion. The dynamics are inherently random rather than deterministic, with trajectories influenced by the noise term σ dW_t. The process has a stationary Gaussian distribution and well-defined statistical properties, but individual sample paths cannot be predicted exactly in the long term.", | |
| "truth_assignment": { | |
| "Chaotic": false, | |
| "Deterministic": false, | |
| "PosLyap": false, | |
| "Sensitive": false, | |
| "StrangeAttr": false, | |
| "PointUnpredictable": true, | |
| "StatPredictable": true, | |
| "QuasiPeriodic": false, | |
| "Random": true, | |
| "FixedPointAttr": false, | |
| "Periodic": false, | |
| "Dissipative": true, | |
| "Bounded": true, | |
| "Mixing": false, | |
| "Ergodic": false, | |
| "HyperChaotic": false, | |
| "Conservative": false, | |
| "HighDimensional": false, | |
| "Multifractal": false, | |
| "HighDimSystem": false, | |
| "ContinuousTime": true, | |
| "DiscreteTime": false, | |
| "DelaySystem": false, | |
| "Forced": false, | |
| "Autonomous": true, | |
| "StrongMixing": false, | |
| "WeakMixing": false | |
| } | |
| } | |