Moderate Deviations Type Evaluation for Integral Functionals of Diffusion Processes
R. Liptser,Vladimir Spokoiny +1 more
TL;DR: In this paper, the authors established a large deviations type evaluation for the family of integral functionals ε −κ T ε 0 Ψ(X ε s)g(ξ ǫ s)ds, where g has zero barycenter with respect to the invariant distribution of the fast diffusion.
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Abstract: We establish a large deviations type evaluation for the family of integral functionals ε −κ T ε 0 Ψ(X ε s)g(ξ ε s)ds, ε 0, where Ψ and g are smooth functions, ξ ε t is a " fast " ergodic diffusion while X ε t is a " slow " diffusion type process, κ ∈ (0, 1/2). Under the assumption that g has zero barycenter with respect to the invariant distribution of the fast diffusion, we derive the main result from the moderate deviation principle for the family (ε −κ t 0 g(ξ ε s)ds) t≥0 , ε 0 which has an independent interest as well. In addition, we give a preview for a vector case.
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Moderate Deviation Principle for Ergodic Markov Chain. Lipschitz Summands
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Large Deviations for Processes with Independent Increments
TL;DR: In this article, the large deviation principle for stochastic processes with stationary and independent increments has been studied under the weak$^\ast$-topology, where the moment generating function of the increments is assumed to lie in the space of functions of bounded variation.