Varadhan estimates for a degenerated convolution semi-group: upper bound
R\'emi L\'eandre
TL;DR
This paper establishes Varadhan estimates for a degenerated jump process with diminishing jumps, employing Malliavin Calculus and Wentzel-Freidlin estimates within semi-group theory.
Contribution
It introduces a novel proof of Varadhan estimates for degenerated jump processes using advanced stochastic calculus and semi-group techniques.
Findings
Proves upper bounds for degenerated jump processes
Utilizes Malliavin Calculus of Bismut type for jumps
Applies Wentzel-Freidlin estimates in semi-group context
Abstract
We give a proof of Varadhan estimates for a degenerated jump process with independent increments with more and more jumps which become smaller and smaller. The proof uses the Malliavin Calculus of Bismut type for jump process in semi-group theory and Wentzel-Freidlin estimates for jump process in semi-group theory.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Spectral Theory in Mathematical Physics