The Annals of Probability

Laplace approximation for rough differential equation driven by fractional Brownian motion

Yuzuru Inahama

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Abstract

We consider a rough differential equation indexed by a small parameter $\varepsilon>0$. 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 $\varepsilon$ tends to zero.

Article information

Source
Ann. Probab., Volume 41, Number 1 (2013), 170-205.

Dates
First available in Project Euclid: 23 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1358951984

Digital Object Identifier
doi:10.1214/11-AOP733

Mathematical Reviews number (MathSciNet)
MR3059196

Zentralblatt MATH identifier
1273.60043

Subjects
Primary: 60G22: Fractional processes, including fractional Brownian motion 60F99: None of the above, but in this section 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Rough path theory Laplace approximation fractional Brownian motion

Citation

Inahama, Yuzuru. Laplace approximation for rough differential equation driven by fractional Brownian motion. Ann. Probab. 41 (2013), no. 1, 170--205. doi:10.1214/11-AOP733. https://projecteuclid.org/euclid.aop/1358951984


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