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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty