simulate-stochastic-processlisted

# Simulate Stochastic Process Simulate sample paths from stochastic processes -- including discrete Markov chains, continuous-time processes, stochastic differential equations, and MCMC samplers -- with convergence diagnostics, variance reduction techniques, and trajectory visualization. ## When to Use - You need to generate sample paths from a stochastic process for estimation, prediction, or visualization - Analytical solutions are intractable and simulation is the only feasible approach - You are running Monte Carlo estimation and need convergence guarantees and uncertainty quantification - You want to validate analytical results (stationary distributions, hitting times) against empirical simulation - You need to sample from a complex posterior distribution using MCMC - You are prototyping a stochastic model before committing to full analytical treatment ## Inputs ### Required | Input | Type | Description | |-------|------|-------------| | `process_type` | string | Type of process: `"dtmc"`, `"ctmc"`, `"random_walk"`, `"brownian_motion"`, `"sde"`, `"mcmc"` | | `parameters` | dict | Process-specific parameters (transition matrix, drift/diffusion coefficients, target density, etc.) | | `n_paths` | integer | Number of independent sample paths to simulate | | `n_steps` | integer | Number of time steps per path (or total MCMC iterations) | ### Optional | Input | Type | Default | Description | |-------|------|---------|-------------| | `initial_state` | scalar/vector | p