Abstract
This chapter introduces the maple software package stochastic consisting of maple routines for stochastic calculus and stochastic differential equations and for constructing basic numerical methods for specific stochastic differential equations, with simple examples illustrating the use of the routines. A website address is given from which the software can be downloaded and where up to date information about installment, new developments and literature can be found.
Keywords
- Stochastic Differential Equation
- Wiener Process
- Partial Differential Operator
- Diffusion Matrix
- Stochastic Calculus
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
L. Arnold, Stochastic Differential Equations. Wiley, New York, 1974.
S.S. Artemiev and T.A. Averina, Numerical Analysis of Systems of Ordinary and of Stochastic Differential Equations. VSP, Utrecht, 1997.
R.E. Crandall, Topics in Advanced Scientific Computation, Springer-Verlag, Heidelberg, 1996.
S.O. Cyganowski, Solving Stochastic Differential Equations with Maple, Maple-Tech Newsletter 3 (2) (1996), 38–40.
S.O. Cyganowski, A MAPLE Package for stochastic differential equations, in “Computational Techniques and Applications: CTAC95” (Editors A. Easton, and R. May ), World Scientific Publishers, Singapore, 1996, 223–230.
S. Cyganowski and P.E. Kloeden, Stochastic stability examined through MAPLE, in Proc. 15th IMACS World Congress, Volume 1: Computational Mathematics (Editor: A. Sydow), Wissenschaft and Technik Verlag, Berlin, 1997, 437–432.
S. Cyganowski, P.E. Kloeden and J. Ombach, From Elementary Probability to Stochastic DEs with MAPLE, Springer-Verlag, Heidelberg, 2001.
S. Cyganowski, P.E. Kloeden and T. Pohl, MAPLE for stochastic differential equations WIAS Berlin, Preprint Nr. 453, 1998. Availability: Postscript 467 KB,http://www.wias-berlin.de/publications/preprints/453
T. Gard, Introduction to Stochastic Differential Equations, Marcel-Dekker, New York, 1988.
W. Gander and J. Hrebicek, Solving Problems in Scientific Computing using Maple and Matlab, Second Edition, Springer- Verlag, Heidelberg, 1995.
W.S. Kendall, Computer algebra and stochastic calculus, Notices Amer. Math. Soc 37 (1990), 1254–1256.
P.E. Kloeden, Stochastic differential equations in environmental modelling and their numerical solution, in Stochastic and Statistical Modelling with Groundwater and Surface Water Applications, (Editor: K. Hipel ), Kluwer Academic Publ., Dordrecht, 1994, 21–32.
P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations Springer-Verlag, Heidelberg, 1992; second revised printing 1999.
P.E. Kloeden and E. Platen, A survey of numerical methods for stochastic differential equations, J. Stoch. Hydrol. Hydraul 3 (1989), 155–178.
P.E. Kloeden and E. Platen, Numerical methods for stochastic differential equations, in Stochastic Modelling and Nonlinear Dynamics: Applications to Mechanical Systems, (Editor: W. Kliemann ), CRC Press, 1994, S. 437–461.
P.E. Kloeden, E. Platen and H. Schurz, Numerical Solution of Stochastic Differential Equations through Computer Experiments, Springer-Verlag, Heidelberg, 1993.
P.E. Kloeden, E. Platen and H. Schurz, The numerical solution of nonlinear stochastic dynamical systems: a brief introduction, J. Bifurcation 6 Chaos 1 (1991), 277–286.
P.E. Kloeden and W.D. Scott, Construction of Stochastic Numerical Schemes through Maple, MapleTech Newsletter 10 (1993), 60–65.
G.N. Milstein, Numerical Integration of Stochastic Differential Equations, Kluwer, Dordrecht, 1995.
G.G. Milstein and M.V. Tret’yakov, Numerical Solution of Differential Equations with Coloured Noise, J. Stat. Physics, 77 (1994) 691–715.
E. Platen, Numerical methods for stochastic differential equations, Acta Numerica, (1999) 197–246.
E. Valkeila, Computer algebra and stochastic analysis, some possibilities, CWI Quarterly 4 (1991), 229–238.
Xu Kedai, Stochastic pitchfork bifurcation: numerical simulations and symbolic calculations using MAPLE, Mathematics and Computers in Simulation 38 (1995), 199–207.
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Cyganowski, S., Grüne, L., Kloeden, P.E. (2001). Maple for Stochastic Differential Equations. In: Blowey, J.F., Coleman, J.P., Craig, A.W. (eds) Theory and Numerics of Differential Equations. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04354-7_3
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DOI: https://doi.org/10.1007/978-3-662-04354-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07533-9
Online ISBN: 978-3-662-04354-7
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