2018/05/25 by Marek Teuerle, Teuerle, Marek
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1805.10027
arxiv created 2018/05/25 · openalex publication_date 2018/05/25 · arxiv updated 2018/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate the asymptotic properties of the wait-first and jump-first Lévy walk with rest, which is a generalization of standard jump-first and jump-first Lévy walk that assumes each waiting time in the model is a sum of two positive random variables. We investigate the asymptotic properties of the theses new-type waiting times. Next we use the previous results of this paper together with continuous mapping approach to establish the main result, which is a functional convergence in Skorokhod \mathbbJ1 topology for the Lévy walks with rests.