An elementary proof for dynamical scaling for certain fractional\n non-homogeneous Poisson processes

2021/03/12 by Markus Kreer, Kreer, Markus · 1 citation
Mathematics · #34E99 #FOS: Mathematics #G.0 #Morphological variations and asymmetry #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2103.07381

openalex publication_date 2021/03/12 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Dynamical scaling is an asymptotic property typical for the dynamics of\nfirst-order phase transitions in physical systems and related to\nself-similarity. Based on the integral-representation for the marginal\nprobabilities of a fractional non-homogeneous Poisson process introduced by\nLeonenko et al. (2017) and generalising the standard fractional Poisson\nprocess, we prove the dynamical scaling under fairly mild conditions. Our\nresult also includes the special case of the standard fractional Poisson\nprocess.\n

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