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arXiv · 1004.1476

A stochastic Taylor-like expansion in the rough path theory

Yuzuru Inahama
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Abstract

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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Yuzuru Inahama. 2010-04-09. A stochastic Taylor-like expansion in the rough path theory. https://arxiv.org/abs/1004.1476

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