sde

sde, a MATLAB code which illustrates the properties of stochastic differential equations (SDE) and some algorithms for handling them, by Desmond Higham.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

sde is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

sde_test

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

brownian_motion_simulation, a MATLAB code which simulates Brownian motion in an M-dimensional region.

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

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

correlation, a MATLAB code which contains examples of statistical correlation functions.

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

pce_ode_hermite, a MATLAB code 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 code 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_rk, a MATLAB code which applies a Runge Kutta (RK) scheme to a stochastic differential equation.

Author:

Desmond Higham

Reference:

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:

• bpath.m computes one simulation of discretized Brownian motion over the time interval [0,1] using 500 time steps and a user specified random number seed.
• bpath_vectorized.m, a second version of BPATH using faster, vectorized commands.
• bpath_average.m, displays the average of 1000 Brownian paths.
• chain.m tests the stochastic Chain Rule.
• em.m, applies the Euler-Maruyama method to integrate a linear SDE.
• emstrong.m tests the strong convergence of the Euler-Maruyama method.
• emweak.m tests the weak convergence of the Euler-Maruyama method.
• milstrong.m tests the strong convergence of the Milstein method.
• stab_asymptotic.m examines the asymptotic stability of the Euler-Maruyama method applied to a stochastic differential equation.
• stab_meansquare.m examines the mean-square stability of the Euler-Maruyama method applied to a stochastic differential equation.
• stochastic_integral_ito.m, approximates the stochastic integral W(t) dW using the Ito integral.
• stochastic_integral_strat.m, approximates the stochastic integral W(t) dW using the Stratonovich integral.