Stochastic Taylor Expansions for Functionals of Diffusion Processes |
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Authors: | Andreas Rößler |
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Affiliation: | 1. Technische Universit?t Darmstadt, Fachbereich Mathematik , Darmstadt, Germany roessler@mathematik.tu-darmstadt.de |
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Abstract: | In this article, a stochastic Taylor expansion of some functional applied to the solution process of an Itô or Stratonovich stochastic differential equation with a multi-dimensional driving Wiener process is given. Therefore, the multi-colored rooted tree analysis is applied in order to obtain a transparent representation of the expansion which is similar to the B-series expansion for solutions of ordinary differential equations in the deterministic setting. Further, some estimates for the mean-square and the mean truncation errors are given. |
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Keywords: | Mean-square approximation Multi-colored rooted tree analysis Stochastic differential equation Stochastic Taylor expansion Strong approximation |
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