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arxiv: 1004.1478 · v2 · pith:TVQOMMDQnew · submitted 2010-04-09 · 🧮 math.PR

Laplace approximation for rough differential equation driven by fractional Brownian motion

classification 🧮 math.PR
keywords differentialequationparameterroughbrowniandrivenfractionalmotion
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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.

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