Laplace approximation for rough differential equation driven by fractional Brownian motion

Abstract

We consider a rough differential equation indexed by a small parameter $\epsilon >0$. When the rough differential equation is driven by fractional Brownian motion with Hurst parameter $H$ ($1/4<H<1/2$), we prove the Laplace-type asymptotics for the solution as the parameter $\epsilon$ tends to zero.

Published in at http://dx.doi.org/10.1214/11-AOP733 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Large deviations for rough paths of the fractional Brownian motion
• Global existence for rough differential equations under linear growth conditions
• Self-similarity and fractional Brownian motions on Lie groups

Cited by in corpus (9)

• On Approximation for Fractional Stochastic Partial Differential Equations on the Sphere
• On the Variational Regularity of Cameron-Martin paths
• Large deviation principle for slow-fast rough differential equations via controlled rough paths
• Large deviations for rough path lifts of Watanabe's pullbacks of delta functions
• Large deviation principle for fractional Brownian motion with respect to capacity
• A stochastic Taylor-like expansion in the rough path theory
• Simple error bounds for the multivariate Laplace approximation under weak local assumptions
• Varadhan Estimates for rough differential equations driven by fractional Brownian motions
• Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions