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Continuous weak approximation for stochastic differential equations

✍ Scribed by Kristian Debrabant; Andreas Rößler

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
256 KB
Volume
214
Category
Article
ISSN
0377-0427

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✦ Synopsis

A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations (SDEs) by general one-step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second order conditions for a class of continuous stochastic Runge-Kutta methods containing the continuous extension of the second order stochastic Runge-Kutta scheme due to Platen are derived. Further, some coefficients for optimal continuous schemes applicable to Itô SDEs with respect to a multi-dimensional Wiener process are presented.

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