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A survey of numerical methods for stochastic differential equations

Kloeden, P.E. and Platen, E. (1989) A survey of numerical methods for stochastic differential equations. Stochastic Hydrology and Hydraulics, 3 (3). pp. 155-178.

Link to Published Version: http://dx.doi.org/10.1007/BF01543857
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Abstract

The development of numerical methods for stochastic differential equations has intensified over the past decade. The earliest methods were usually heuristic adaptations of deterministic methods, but were found to have limited accuracy regardless of the order of the original scheme. A stochastic counterpart of the Taylor formula now provides a framework for the systematic investigation of numerical methods for stochastic differential equations. It suggests numerical schemes, which involve multiple stochastic integrals, of higher order of convergence. We shall survey the literature on these and on the earlier schemes in this paper. Our discussion will focus on diffusion processes, but we shall also indicate the extensions needed to handle processes with jump components. In particular, we shall classify the schemes according to strong or weak convergence criteria, depending on whether the approximation of the sample paths or of the probability distribution is of main interest.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Springer-Verlag
URI: http://researchrepository.murdoch.edu.au/id/eprint/31666
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