sde_test

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

Licensing:

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

Related Data and Programs:

sde, an Octave code which illustrates properties of stochastic ordinary differential equations (SODE's), and common algorithms for their analysis, including the Euler method, the Euler-Maruyama method, and the Milstein method, by Desmond Higham;

Source Code:

• sde_test.m, calls all the tests.
• sde_test.sh, runs all the tests.
• sde_test.txt, the output file.

• stochastic_integral_ito_test.m, tests stochastic_integral_ito.
• stochastic_integral_strat_test.m, tests stochastic_integral_strat.

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

• bpath.png, an image of the computed path for BPATH.
• bpath_vectorized.png, an image of the computed path for BPATH_VECTORIZED.
• bpath_average.png, an image of the averaged paths for BPATH_AVERAGE.
• 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.