# Student Probability Seminar

#### Schilder's theorem

**Speaker:**
Jeanne Boursier

**Location:**
Warren Weaver Hall 512

**Date:**
Wednesday, November 7, 2018, noon

**Synopsis:**

In this talk we will discuss a large deviation principle for Brownian motion, named Schilder's theorem. This result orginates from the paper "Some asymptotic formulas for Wiener integrals", written by M. Schilder in 1962, which was reworded in the language of the modern theory of large deviations developed at the same time. There are many enhancements of Schilder's theorem but we will only focus on the classical one, where the Brownian motion is viewed as a random variable on the space of continuous functions, endowed with the infinite-norm topology. We will present a short self-contained proof, based on the Girsanov formula and on a piecewise linear approximation of the path. No specific knowledge about large deviations is needed.