Alexandre Pannier
Imperial College and Princeton University

Pathwise large deviations for white noise chaos expansions

We consider a family of continuous processes, measurable with respect to a white noise measure, and characterised by their Wiener chaos expansion. We provide sufficient conditions for their large deviations principle to hold in path space, thereby refreshing a problem left open by Pérez-Abreu in 1993 in the Brownian motion case. The proof is based on the weak convergence approach to large deviations: it involves demonstrating the convergence in distribution of certain perturbations of the original process, and thus the main difficulties lie in analysing and controlling the perturbed multiple stochastic integrals. Moreover, adopting this representation offers a new perspective on pathwise large deviations and induces a variety of applications thereof.

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