Contents:

The MAPLE stochastic package offers a number of MAPLE routines for stochastic differential equations. The names of the functions are



  LO           SL0         LJ         MLJ               LFP
  itoformula   chainrule   correct    conv              explicit
  linearsde    reducible   colour     comm1             comm2
  linearize    momenteqn   position   sphere 
  
  Euler        Milstein    milcomm    Taylor1hlf        Taylor2
  wkeuler      wktay2      wktay3
  
  pa           ap          bpb        pmatrix2pvector   pvector2pmatrix

Downloading and Installation

• For Maple 9 or newer, download the file stochastic9 (hold down shift when selecting the link or select "SaveAs" from the file menu after you have selected the link), and save it into some directory dir.


• Type
  read "dir/stochastic9"; on UNIX/LINUX or Windows systems OR
  read "dir:stochastic9"; on Macintosh systems
  at the MAPLE prompt to load the file into MAPLE
  Caution:
  • On Macintosh computers it might be necessary to open the file in a text editor (e.g. BBedit) and save it under the same name as Simple Text
  • Some browsers, especially on Windows systems, automatically save the file under "stochastic9.html". Try
    read "dir/stochastic9.html"; if you encounter difficulties reading the package
  • On Windows systems the components of dir have to be seperated by "/" (not by "\" as usually)
  • On UNIX/LINUX you can omit dir/ when you start MAPLE from the directory dir


• Type
  with(stochastic);
at the MAPLE prompt to load the whole package.
  Alternatively, you can load single functions from the package typing
  with(stochastic, functionname);
  or access each function in the package using the long form
  stochastic[functionname];
  This might be necessary when there is a conflict between a package function name and another function used in the same session.



• For Maple 6, 7, 8, proceed as above using the file stochastic6.
• For Maple V, Release 5.1, proceed as above using the file stochastic5.

Recent Changes:

• October 26, 2006: The package "stochastic9" and "stochplot9" were tested with Maple 10 and found to be working. If, however, you discover any problems, please let us know.


• June 21, 2005: The new package "stochastic9" was placed here, which works with Maple 9 and 9.5.
  Many thanks to Stefanie Schönbrodt who analyzed the problem and made the necessary changes!


• December 11, 2003: We fixed a bug in the itoformula-routine, which caused wrong results when the number of stochastic processes was larger than the dimension of the SDE.
  Many thanks to Björgvin Sigurdsson for reporting this error and providing a solution!


• October 30, 2003: The new package "stochastic6" was placed here. Even though "stochastic5" runs without errors on Maple 6, 7 and 8 and produces correct output on the screen, some formulas give wrong results when used as an input to other Maple routines.
  Many thanks to Jerzy Ombach who corrected this problem!

Documentation and Related Papers:

• The most comprehensive and up-to-date paper on the stochastic package is
  
          Sasha Cyganowski, Lars Grüne, Peter E. Kloeden:
          MAPLE for Stochastic Differential Equations
  
  Although written in a scientific style, this paper serves as a manual for the stochastic package. The related demo worksheets maplesde.mw (Maple 9 and newer) and maplesde.mws (Maple 8 and older) contain all the examples from this paper
  
  
• More literature can be found on Peter Kloeden's page on MAPLE for SDEs
  
  
• Software for Springer Books on Numerical and Symbolical Methods for SDEs

The stochplot package:

• stochplot9 (Maple 9, 9.5, 10)
• stochplot6V3 (Maple 6, 7, 8)
• stochplot5 (Maple V, Release 5.1)


• stochplot9_demo.mw (Demo worksheet illustrating the use of "stochplot9", for Maple 9, 9.5, 10)
• stochplot6V3_demo.mws (Demo worksheet illustrating the use of "stochplot6V3", for Maple 6, 7, 8)
• stochplot_demo.mws (Demo worksheet illustrating the use of "stochplot5", for Maple V, Release 5.1)

Recent Changes:

• June 21, 2005: The package "stochplot9" and the related demo worksheet "stochplot9_demo.mw" were placed here. These are the same as the "6V3" versions except for the new "mw" format of the demo worksheet.


• October 5, 2004: The package "stochplot6V3" and the related demo worksheet "stochplot6V3_demo.mws" were placed here. These files replace the "V2" versions and contain the new routine "stochplot_time" for time dependent one dimensional SDEs.


• October 30, 2003: The package "stochplot6V2" and the related demo worksheet "stochplot6V2_demo.mws" were placed here. These files replace the old versions without version numbers and are compatible with the "stochastic6" package.

Note:

• Since the stochplot packages are only suitable for 1d SDEs, they have a somewhat limited applicability and are mainly useful as templates for the development of more general routines. If you have written such routines and want to make them available to other users please contact me. I'll be happy to place them on this web site.

Additional Material:

• moreschms (Explicit weak order 2 and implicit weak order 2 schemes)
• weakimp2 (Implicit weak order 2 scheme)
• wktay2 (Weak Taylor scheme of order 2)

Related Work:

• D.J. Higham has written several MATLAB routines for Stochastic DEs. Preprints of the related papers are available from D.J. Higham's publications page. The joint paper D.J. Higham, P.E. Kloeden, "MAPLE and MATLAB for Stochastic Differential Equations in Finance" is also available as paper number 8 on Peter Kloeden's page on MAPLE for SDEs.


• MAPLE routines for jump-diffusion SDEs are described in the paper S. Cyganowski, L. Grüne and P.E. Kloeden, MAPLE for Jump-Diffusion Stochastic Differential Equations in Finance.


• xmds, a free software package for solving stochastic (and deterministic) ODEs and PDEs

Contact:

Feel free to email us for comments:


Lars Grüne (follow the link to see my e-mail address)