sde

sde, a Python code which illustrates properties of stochastic ordinary differential equations (SDE), and common algorithms for their analysis, including the Euler method, the Euler-Maruyama method, and the Milstein method, 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.

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Author:

Original MATLAB version by Desmond Higham. This version by John Burkardt.

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:

• sde.py, the source code.
• sde.sh, runs all the tests.
• sde.txt, the output file.

• bpath.png, an image of the computed path for BPATH.
• bpath1.png
• bpath2.png
• bpath_average.png, an image of the averaged paths for BPATH_AVERAGE.
• bpath_vectorized.png, an image of the computed path for BPATH_VECTORIZED.
• chain.png, an image comparing solutions done with and without the chain rule.
• em.png, an image of a true solution versus the Euler-Maruyama estimate.
• emstrong.png, an image of the strong convergence of the Euler-Maruyama error with stepsize.
• emweak0.png, an image of the weak convergence of the standard Euler-Maruyama method.
• emweak1.png, an image of the weak convergence of the weak Euler-Maruyama method.
• milstrong.png, an image of the strong convergence of the Milstein method.
• stab_asymptotic.png, an image of an asymptotic stability check.
• stab_meansquare.png, an image of a meansquare stability check.
• stab1.png
• stab2.png