Markov processes with redistribution

I. Grigorescu, Min Kang

Research output: Contribution to journalArticle

Abstract

We study a class of stochastic processes evolving in the interior of a set D according to an underlying Markov kernel, undergoing jumps to a random point x in D with distribution vξ(dx) as soon as they reach a point £ outside D. We give conditions on the family of measures vε(dx) preventing that infinitely many jumps occur in finite time (explosiveness), conditions for ergodicity and the existence of a spectral gap. The setup is applied to a multitude of models considered recently, including particle systems like the Fleming -Viot branching process and a new variant of the Bak-Sneppen dynamics from evolutionary biology. The last part of the paper is expository and discusses the relation with quasi-stationary distributions.

Original languageEnglish (US)
Pages (from-to)497-520
Number of pages24
JournalMarkov Processes and Related Fields
Volume19
Issue number3
StatePublished - Dec 1 2013

Keywords

  • Doeblin condition
  • Fleming-Viot branching process
  • Jump diffusion process
  • Quasi-stationary distribution qsd

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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