# src/DiffEq/OrnsteinUhlenbeck.h file

System of Ornstein-Uhlenbeck SDEs.

### Contents

• Reference

This file implements the time integration of a system of stochastic differential equations (SDEs), with linear drift and constant diffusion, whose invariant is the joint normal distribution.

In a nutshell, the equation integrated governs a set of scalars, , , as

with parameter vectors , , and symmetric positive semi-definite diffusion matrix . Here is an isotropic vector-valued Wiener process with independent increments. The invariant distribution is the joint normal distribution. This system of SDEs consists of N coupled equations, each being a single-variate Ornstein-Uhlenbeck process.

From the Fokker-Planck equation, equivalent to the SDE above, the equations governing the means, , are

while the equation governing the covariance matrix, , is

## Namespaces

namespace walker
Walker declarations and definitions.

## Classes

template<class Init, class Coefficients>
class walker::OrnsteinUhlenbeck
Ornstein-Uhlenbeck SDE used polymorphically with DiffEq.