Large Deviations for Brownian Motion in Evolving Riemannian Manifolds

Versendaal, R.

Large Deviations for Brownian Motion in Evolving Riemannian Manifolds

Journal article (2021)

Authors

R. Versendaal Applied Probability

Research Group

Applied Probability

Large deviations Anti-development Evolving manifold Frame bundle Freidlin – Wentzell theory G(t)-Brownian motion Horizontal lift Schilder’s theorem Time-dependent geometry

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Published Date

2021

Language

English

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Research Group

Applied Probability

Abstract

We prove large deviations for g(t)-Brownian motion in a complete, evolving Riemannian manifold M with respect to a collection {g(t)}_t_∈[0,1] of Riemannian metrics, smoothly depending on t. We show how the large deviations are obtained from the large deviations of the (time-dependent) horizontal lift of g(t)-Brownian motion to the frame bundle F M over M. The latter is proved by embedding the frame bundle into some Euclidean space and applying Freidlin – Wentzell theory for diffusions with time-dependent coefficients, where the coefficients are jointly Lipschitz in space and time.

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