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August 2022 Pathwise large deviations for white noise chaos expansions
Alexandre Pannier
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Bernoulli 28(3): 1961-1985 (August 2022). DOI: 10.3150/21-BEJ1407

Abstract

We consider a family of continuous processes {Xε}ε>0 which are measurable with respect to a white noise measure, take values in the space of continuous functions C([0,1]d:R), and have the Wiener chaos expansion

Xε=n=0εnIn(fnε).

We provide sufficient conditions for the large deviations principle of {Xε}ε>0 to hold in C([0,1]d:R), thereby refreshing a problem left open by Pérez–Abreu (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.

Acknowledgements

The author expresses his sincere gratitude to Antoine Jacquier for his guidance and support, and to Eyal Neuman and Amarjit Budhiraja for stimulating discussions.

Citation

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Alexandre Pannier. "Pathwise large deviations for white noise chaos expansions." Bernoulli 28 (3) 1961 - 1985, August 2022. https://doi.org/10.3150/21-BEJ1407

Information

Received: 1 March 2021; Published: August 2022
First available in Project Euclid: 25 April 2022

Digital Object Identifier: 10.3150/21-BEJ1407

Keywords: large deviations , Malliavin calculus , multiple stochastic integrals , weak convergence , white noise measure , Wiener Chaos

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Vol.28 • No. 3 • August 2022
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