A stochastic Taylor-like expansion in the rough path theory

Details A stochastic Taylor-like expansion in the rough path theory A stochastic Taylor-like expansion in the rough path theory

2010-04-09

arxiv.org/abs/1004.1476v1

Mathematics

Probability

Scientific paper

In this paper we establish a Taylor-like expansion in the context of the
rough path theory for a family of It ^{o} maps indexed by a small parameter. We
treat not only the case that the roughness $p$ satisfies $[p]=2$, but also the
case that $[p] ge 3$. As an application, we discuss the Laplace asymptotics for
It^{o} functionals of Brownian rough paths.

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