Module stochastic_processes

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Stochastic processes for simulation and financial/physical modeling.

This module provides implementations of key stochastic processes used in computational physics, quantitative finance, and statistical modeling:

BrownianMotion — standard Wiener process path generation
GeometricBrownianMotion — log-normal GBM (Black-Scholes)
OrnsteinUhlenbeck — mean-reverting SDE (OU process)
JumpDiffusion — Merton model with Poisson jumps
FractionalBrownianMotion — fBm with Hurst exponent H
CoxIngersollRoss — CIR interest rate model (Milstein scheme)
HestonModel — stochastic volatility (Euler-Maruyama)
LevyStableProcess — stable distribution parameters
BranchingProcess — Galton-Watson branching process
MarkovChain — discrete-time Markov chain utilities
PoissonProcess — homogeneous and inhomogeneous Poisson
Variance reduction: antithetic_variates, control_variate_estimator, quasi_monte_carlo

Structs§

BranchingProcess: Galton-Watson branching process.
BrownianMotion: Standard Wiener process (Brownian motion) W(t).
CoxIngersollRoss: Cox-Ingersoll-Ross (CIR) interest rate model.
FractionalBrownianMotion: Fractional Brownian motion with Hurst exponent H in (0, 1).
GeometricBrownianMotion: Geometric Brownian Motion (GBM) for log-normal asset/particle dynamics.
HestonModel: Heston stochastic volatility model.
JumpDiffusion: Merton jump-diffusion model: GBM plus compound Poisson jumps.
LevyStableProcess: Lévy stable process with four parameters.
MarkovChain: Discrete-time finite Markov chain.
OrnsteinUhlenbeck: Ornstein-Uhlenbeck mean-reverting process.
PoissonProcess: Homogeneous and inhomogeneous Poisson processes.

antithetic_variates: Antithetic variates estimator.
control_variate_estimator: Control variate estimator.
halton: Compute the i-th element of the Halton sequence in the given base.
quasi_monte_carlo: Quasi-Monte Carlo: Halton sequence in base 2 and 3 for 2D integration.