sde

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

The original version of these routines is available at "https://www.maths.strath.ac.uk/~aas96106/algfiles.html".

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

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

Related Data and Programs:

sde_test

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

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

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

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

correlation, an Octave code which contains examples of statistical correlation functions.

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

pce_ode_hermite, an Octave 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, an Octave 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, an Octave 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.