Stochastic Differential Equations

SDE is a MATLAB library which illustrates the properties of stochastic differential equations and some algorithms for handling them, by Desmond Higham.

The original version of these routines is available at "".


SDE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BLACK_SCHOLES, a MATLAB library which implements some simple approaches to the Black-Scholes option valuation theory, by Desmond Higham.

BROWNIAN_MOTION_SIMULATION, a MATLAB program which simulates Brownian motion in an M-dimensional region.

CNOISE, a MATLAB library which generates samples of noise obeying a 1/f^alpha power law, by Miroslav Stoyanov.

COLORED_NOISE, a MATLAB library which generates samples of noise obeying a 1/f^alpha power law.

CORRELATION, a MATLAB library which contains examples of statistical correlation functions.

ORNSTEIN_UHLENBECK, a MATLAB library which approximates solutions of the Ornstein-Uhlenbeck stochastic differential equation (SDE) using the Euler method and the Euler-Maruyama method.

PCE_BURGERS, a MATLAB program which defines and solves a version of the time-dependent viscous Burgers equation, with uncertain viscosity, using a polynomial chaos expansion in terms of Hermite polynomials, by Gianluca Iaccarino.

PCE_LEGENDRE, a MATLAB program which assembles the system matrix associated with a polynomal chaos expansion of a 2D stochastic PDE, using Legendre polynomials;

PCE_ODE_HERMITE, a MATLAB program which sets up a simple scalar ODE for exponential decay with an uncertain decay rate, using a polynomial chaos expansion in terms of Hermite polynomials.

PINK_NOISE, a MATLAB library which computes a "pink noise" signal obeying a 1/f power law.

STOCHASTIC_DIFFUSION, MATLAB functions which implement several versions of a stochastic diffusivity coefficient.

STOCHASTIC_GRADIENT_ND_NOISE, a MATLAB program which solves an optimization problem involving a functional over a system with stochastic noise.

STOCHASTIC_RK, a MATLAB library which applies a Runge Kutta (RK) scheme to a stochastic differential equation.


Desmond Higham


  1. Desmond Higham,
    An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations,
    SIAM Review,
    Volume 43, Number 3, September 2001, pages 525-546.

Source Code:

Examples and Tests:

A number of graphics images are created by the example programs:

You can go up one level to the MATLAB source codes.

Last revised on 18 September 2012.