Open AccessLimit properties of Lévy walks
Author(s) -
Marcin Magdziarz,
Tomasz Zorawik
Publication year - 2020
Publication title -
journal of physics. a, mathematical and theoretical
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.787
H-Index - 163
eISSN - 1751-8121
pISSN - 1751-8113
DOI - 10.1088/1751-8121/abc43c
Subject(s) - mathematics , limit (mathematics) , conjecture , martingale (probability theory) , statistical physics , representation (politics) , random walk , diffusion , mathematical analysis , pure mathematics , statistics , physics , politics , political science , law , thermodynamics
In this paper we study properties of the diffusion limits of three different models of Lévy walks (LW). Exact asymptotic behavior of their trajectories is found using LePage series representation. We also prove an existing conjecture about total variation of LW sample paths. Based on this conjecture we verify martingale properties of the limit processes for LW. We also calculate their probability density functions and apply this result to determine the potential density of the associated non-symmetric α -stable processes. The obtained theoretical results for continuous LW can be used to recognize and verify this type of processes from anomalous diffusion experimental data. In particular they can be used to estimate parameters from experimental data using maximum likelihood methods.