Limit theorems for local times and applications to SDEs with jumps

Aleksandar Mijatović and Gerónimo Uribe Bravo

Stochastic Processes and their Applications, 2022, vol. 153, issue C, 39-56

Abstract: Consider a stochastic process X, regenerative at a state x which is instantaneous and regular. Let L be a regenerative local time for X at x. Suppose furthermore that X can be approximated by discrete time regenerative processes Xn for which x is accessible. We give conditions on X and Xn so that the naturally defined local time of Xn (which counts the quantity of visits to x) converges weakly to L. This limit theorem generalizes previous invariance principles that have appeared in the literature. Furthermore, it allows one to prove novel invariance principles for local times of regenerative processes converging to diffusions or to solutions of SDEs with jumps.

Keywords: local time; invariance principle; regenerative processes; stochastic differential equations with jumps (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.06.022

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