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Journal of Theoretical Probability

, Volume 23, Issue 3, pp 671–714 | Cite as

A Stochastic Taylor-Like Expansion in the Rough Path Theory

  • Yuzuru Inahama
Article

Abstract

In this paper, we establish a Taylor-like expansion in the context of rough path theory for a family of Itô 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]≥3. As an application, we discuss the Laplace asymptotics for Itô functionals of Brownian rough paths.

Keywords

Rough path Itô map Taylor expansion Laplace asymptotics 

Mathematics Subject Classification (2000)

60H14 60F99 

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityNagoyaJapan

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