Large deviations for stochastic flows of diffeomorphisms

TL;DR

This paper establishes a large deviation principle for stochastic flows of diffeomorphisms in the small noise limit and applies it to Bayesian image matching, demonstrating an approximate maximum likelihood property.

Contribution

It introduces a large deviation framework for stochastic flows and connects it to Bayesian image matching with an optimization approach.

Findings

Large deviation principle for stochastic flows established

Application to Bayesian image matching demonstrated

Approximate maximum likelihood property shown

Abstract

A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property is shown for the solution of an optimization problem involving the large deviations rate function.