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MAPLE Stochastic Package
The MAPLE Stochastic Package
by Sasha Cyganowski
Maintained by Lars Grüne
Extensions and Updates by
Thomas Pohl, Lars Grüne and Stefanie Schönbrodt
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
We provide the stochastic package for Maple 613 and for Maple
V, Release 5.1.

For Maple 9 or newer, download the file stochastic9
(e.g., by right clicking the link and selecting "Save Link As" from the file menu), and save it into some directory dir.

Type
read "dir/stochastic9";
at the MAPLE prompt to
load the file into MAPLE
Caution:
 Some browsers 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 most systems you can omit
dir/
when dir
is the current directory

Type
with(stochastic);
at the MAPLE prompt to activate whole package.
Alternatively, you can
activate 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:
 July 1, 2011: The packages "stochastic9" and "stochplot9"
were tested with Maple 13 and found to be working. If, however, you
discover any problems, please let us know. Furthermore, all
outdated links on this page were updated.
 October 26, 2006: The packages "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!
We would also like to thank all the users who reported
bugs and problems in older versions!
Documentation and Related Papers:
The
stochplot package:
The "stochplot..."files contain procedures for plotting approximate
solutions curves for onedimensional SDES.
The output of any of the numerical scheme procedures
from the stochastic package can be used as input. The corresponding
demo worksheets demonstrate the use of these routines.
The source code for these packages can be loaded into a Maple worksheet
using the read
command as described above.
 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:
The following files contain additional numerical schemes for SDEs.
You should be familiar with the subject if you want to use them.
No guarantee is given for the
correctness of these algorithms, they are placed here as
they may be of some benefit to others, but they are not part of the
"stochastic" package.
The source code for these packages can be loaded into a Maple worksheet
using the read
command as described above.
 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:
Contact:
Feel free to email us for comments:
Lars
Grüne (follow the link to see my email address)
Lars
Grüne
Last Change: July 1, 2011
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