We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the (k-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies a propagation of chaos result in a space of rough paths and allows for a robust analysis of the particle system and its McKean-Vlasov type limit, as shown in two corollaries.
The enhanced Sanov theorem and propagation of chaos / J. Deuschel, P.K. Friz, M. Maurelli, M. Slowik. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - 128:7(2018), pp. 2228-2269.
The enhanced Sanov theorem and propagation of chaos
M. Maurelli;
2018
Abstract
We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the (k-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies a propagation of chaos result in a space of rough paths and allows for a robust analysis of the particle system and its McKean-Vlasov type limit, as shown in two corollaries.
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Enhanced_Sanov_reviewed.pdf
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DeuFriMauSlo2018.pdf
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