Large deviation principle for bridges of degenerate diffusions

TL;DR

This paper establishes a large deviation principle for bridges of subelliptic diffusions on compact manifolds as the travel time approaches zero, revealing their asymptotic behavior in a Holder continuous function space.

Contribution

It proves a large deviation principle for degenerate diffusion bridges with distinct endpoints, providing new insights into their small-time asymptotics.

Findings

Bridges satisfy a large deviation principle in Holder space

Identifies deterministic first order asymptotics of bridge distributions

Applicable under generic endpoint conditions

Abstract

We prove that bridges of subelliptic diffusions on a compact manifold, with distinct ends, satisfy a large deviation principle in a space of Holder continuous functions, with a good rate function, when the travel time tends to 0. This leads to the identification of the deterministic first order asymptotics of the distribution of the bridge under generic conditions on the endpoints of the bridge.