Journal Article10.5705/SS.2013.134
Moderate Deviations for Interacting Processes
TL;DR: In this article, moderate deviations of the occupation measures for both the strong τ -topology on the space of finite and bounded measures as well as for corresponding stochastic processes on some class of functions equipped with the uniform topology are discussed.
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Abstract: This article is concerned with moderate deviation principles of a class of interacting empirical processes. We derive an explicit description of the rate function, and we illustrate these results with Feynman-Kac particle models arising in nonlinear filtering, statistical machine learning, rare event analysis, and computational physics. We discuss functional moderate deviations of the occupation measures for both the strong τ -topology on the space of finite and bounded measures as well as for the corresponding stochastic processes on some class of functions equipped with the uniform topology, yielding the first results of this type for mean field interacting processes. Our approach is based on an original semigroup analysis combined with Orlicz norm inequalities, stochastic perturbation techniques, and projective limit large deviation methods.
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Citations
Moderate Deviation Principles for Weakly Interacting Particle Systems
Amarjit Budhiraja,Ruoyu Wu +1 more
TL;DR: In this article, the moderate deviation principle for empirical measure processes associated with weakly interacting Markov processes is established in the path space of an appropriate Schwartz distribution space and in the space of the Hilbert space of square summable sequences.
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Moderate Deviation Principles for Weakly Interacting Particle Systems
Amarjit Budhiraja,Ruoyu Wu +1 more
TL;DR: In this paper, the moderate deviation principle for empirical measure processes associated with weakly interacting Markov processes is established in terms of a large deviation principle with an appropriate speed function, for suitably centered and normalized empirical measures.
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A second order analysis of McKean–Vlasov semigroups
Marc Arnaudon,P. Del Moral +1 more
TL;DR: In this article, a second order differential calculus is proposed to analyze the regularity and stability properties of the distribution semigroup associated with McKean-Vlasov diffusions.
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Central limit theorem and Self-normalized Cram\'er-type moderate deviation for Euler-Maruyama Scheme
Jianya Lu,Yuzhen Tan,Lihu Xu +2 more
TL;DR: In this article, a stochastic differential equation and its Euler-Maruyama (EM) scheme admit a unique invariant measure, denoted by π$ and π_\eta$ respectively, which is the step size of the EM scheme.
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Moderate deviation principles for importance sampling estimators of risk measures
TL;DR: Using a delta method for large deviations, combined with classical large deviation techniques, the moderate deviation principle is obtained for importance sampling estimators of two of the most common risk measures: value at risk and expected shortfall.
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