Self-similar stochastic processes with stationary increments as limits of particle systems

Abstract

We give a particle picture interpretation of two recently discovered classes of self-similar stable processes with stationary increments studied by Samorodnitsky et al. and Dombry and Guillotin-Plantard. We study the occupation times of certain Poissonian systems of particles with ±1 charges and i.i.d. heavy-tailed weights, moving independently according to Lévy processes. We also obtain a new class of self-similar stable processes.

KEYWORDS:

• Local times
• Lévy processes
• stable self-similar processes
• particle systems
• weak convergence

2000 Mathematics Subject Classification:

• Primary: 60G18 Secondary: 60F17

Additional information

Funding

Research supported in part by National Science Center, Poland [grant 2017/25/N/ST1/00368].