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The numerical solution of stochastic differential equations

Published online by Cambridge University Press:  17 February 2009

P. E. Kloeden
Affiliation:
Department of Mathematics, Monash University, Clayton, Vic. 3168, Australia
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Abstract

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A method is proposed for the numerical solution of Itô stochastic differential equations by means of a second-order Runge–Kutta iterative scheme rather than the less efficient Euler iterative scheme. It requires the Runge–Kutta iterative scheme to be applied to a different stochastic differential equation obtained by subtraction of a correction term from the given one.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Clements, D. J. and Anderson, B. D. O., “Well-behaved Itô equations with simulations always misbehaved”, IEEE Trans. Automatic Control AC-18 (1973), 676677.CrossRefGoogle Scholar
[2]Henrici, P., Discrete Variable Methods in Ordinary Differential Equations, John Wiley and Sons, New York (1965).Google Scholar
[3]Kuo, S. S., Computer Applications of Numerical Methods, Addison-Wesley, Reading, Mass. (1972).Google Scholar
[4]McShane, E. J., “Stochastic differential equations and models of random processes”, in Proc. Sixth Berkeley Symp. Probability and Mathematical Statistics (1971) 263–294.CrossRefGoogle Scholar
[5]Rao, N. J., Borwankar, J. D. and Ramkrishna, D., “Numerical solution of Itô integral equations”, SIAM J. Control 12 (1974), 124139.CrossRefGoogle Scholar
[6]Stratonovich, R. L., “A new representation for stochastic integrals and equations”, SIAM J. Control 4 (1966), 362371.CrossRefGoogle Scholar
[7]Wong, E., Stochastic Processes in Information and Dynamical Systems, McGraw-Hill, New York (1971).Google Scholar
[8]Wright, D. J., “The digital simulation of stochastic differential equations”, IEEE Trans. Automatic Control AC-19 (1974), 7576.CrossRefGoogle Scholar