This is an updated version of the 2013 work presented by Dr Alexander Lundervold (http://alexander.lundervold.com/) on GitHub (see https://github.com/alu042/SDE-higham) and the MatLab files Prof Des Higham (https://www.maths.ed.ac.uk/~dhigham/) makes available on his homepage (https://www.maths.ed.ac.uk/~dhigham/algfiles.html). The code we present here is the respective code found on those two locations updated/converted to run in Python 3 and including the typo corrections as detailed by Prof Des Higham on his website.
We thank Prof Higham for kindly giving us permision to host the MATLAB files here.
Modified from the MATLAB versions in Higham “An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations”, SIAM Review, Vol. 43, No. 3, 2001. https://doi.org/10.1137/S0036144500378302. Downloadble version from Des Higham’s website: http://personal.strath.ac.uk/d.j.higham/Plist/P42.pdf
Details about the algorithms can be found in the paper.
| Filename | Description |
|---|---|
| bpath1 | Naive simulation of a Brownian path |
| bpath2 | Simulation of a Brownian path |
| bpath3 | Function along a Brownain path |
| stint | Approximate stochastic integrals |
| em | Euler-Maruyama method on linear SDE |
| emstrong | Test strong convergence of Euler-Maruyama |
| emweak | Test weak convergence of Euler-Maruyama |
| milstrong | Test strong convergence of Milstein method |
| stab | Mean-square and asymptotic stability test for E-M |
| chain | Test stochastic chain rule |
| milstein-3d | Milstein’s method applied to a 3D SDE (not part of SIAM paper) |