Bessel-like birth-death process [article]

Vygintas Gontis, Aleksejus Kononovicius
2019 arXiv   pre-print
We do consider models of the population or opinion dynamics which result in non-linear stochastic differential equations (SDEs) exhibiting spurious long-range memory. In this context, the correspondence between the description of birth-death processes as continuous-time Markov chains and continuous SDEs is of high importance for the alternatives of modeling. We propose and generalize Bessel-like birth-death process having clear representation by SDEs. The new process helps to integrate
more » ... ves of description and to derive equations for the probability density function (PDF) of burst and inter-burst duration of the proposed continuous time birth-death processes. This PDF might be used to discriminate between spurious memory and true long-range memory in complex systems exhibiting continuing fluctuations.
arXiv:1904.13064v1 fatcat:iauljwkjwjfhvg2mzvxgbyf2qq