Sample-path large deviations for Lévy processes and random walks with Weibull increments

2017/10/11 by Bazhba, Mihail, Blanchet, Jose, Rhee, Chang-Han +1
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1710.04013

Abstract

We study sample-path large deviations for Lévy processes and random walks with heavy-tailed jump-size distributions that are of Weibull type. Our main results include an extended form of an LDP (large deviations principle) in the J₁ topology, and a full LDP in the M₁' topology. The rate function can be represented as the solution to a quasi-variational problem. The sharpness and applicability of these results are illustrated by a counterexample proving the nonexistence of a full LDP in the J₁ topology, and by an application to a first passage problem.

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