Asymptotics of transition densities for L\'evy processes with stochastic resetting

Kacper Budnik; Tomasz Grzywny; Paweł Sztonyk

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arXiv · 2607.13273

Asymptotics of transition densities for L\'evy processes with stochastic resetting

Kacper Budnik·Tomasz Grzywny·Paweł Sztonyk

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Abstract

We derive an explicit representation for the distribution of a L\'evy process with total stochastic resetting and use it to investigate the asymptotic behaviour of the corresponding transition densities. The proposed approach applies to several important classes of L\'evy processes, including relativistic stable processes, and yields new asymptotic estimates for their transition densities.

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Kacper Budnik, Tomasz Grzywny, Paweł Sztonyk. 2026-07-14. Asymptotics of transition densities for L\'evy processes with stochastic resetting. https://arxiv.org/abs/2607.13273

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