##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability

## Yuzuru Inahama

#### Osaka University

## Laplace's method for differential equations in the rough path theory

##### Abstract:

I will prove aymptotic results (large deviation and Laplace's method) for the laws of solutions of (formal stochastic) differential equations in the rough path sense. My result can be regarded as a "rough path version" of famous results for finite dimensional SDEs. However, formulated on a general Banach space, my results contain something new. Examples include: (1) solutions of SDEs on M-type 2 Banach spaces, and (2) heat processes (or heat kernel measures) on loop spaces.

Host: Jason Schweinsberg

### January 26, 2006

### 9:00 AM

### AP&M 6218

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