A Chen-Fliess approximation for diffusion functionals

Details A Chen-Fliess approximation for diffusion functionals A Chen-Fliess approximation for diffusion functionals

2011-10-11

arxiv.org/abs/1110.2481v2

Mathematics

Probability

extended introduction, references added, changed title, minor typos fixed

Scientific paper

We show that an interesting class of functionals of stochastic differential equations can be approximated by a Chen-Fliess series of iterated stochastic integrals and give a L^{2} error estimate, thus generalizing the standard stochastic Taylor expansion. The coefficients in this series are given a very intuitive meaning by using functional derivatives, recently introduced by B. Dupire.

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