Asymptotics of transition densities for Lévy processes with stochastic resetting

Kacper Budnik; Tomasz Grzywny; Paweł Sztonyk

Asymptotics of transition densities for Lévy processes with stochastic resetting

Probability 2026-07-14 v1

Authors: Kacper Budnik , Tomasz Grzywny , Paweł Sztonyk

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.

Keywords

Lévy processes stochastic resetting transition densities asymptotics relativistic stable processes

Cite

@article{arxiv.2607.13273,
  title  = {Asymptotics of transition densities for Lévy processes with stochastic resetting},
  author = {Kacper Budnik and Tomasz Grzywny and Paweł Sztonyk},
  journal= {arXiv preprint arXiv:2607.13273},
  year   = {2026}
}