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hal-00710217, version 1

Markov Processes with Restart

Konstantin Avrachenkov (, http://www-sop.inria.fr/mistral/personnel/K.Avrachenkov/me.html) 1, Alexei Piunovskiy () a, 2, Zhang Yi 2

N° RR-8000 (2012)

  • a –  University of Liverpool
  • 1 :  MAESTRO (INRIA Sophia Antipolis)

  • INRIA – Université Montpellier II - Sciences et techniques France
  • 2 :  Department of Mathematical Sciences [Liverpool]
  • http://www.liv.ac.uk/maths/
    Liverpool University The University of Liverpool Mathematical Sciences Building Liverpool, L69 7ZL Royaume-Uni

Références bibliographiques

  • Type de publication : Rapports
  • Domaine : Informatique/Réseaux et télécommunications
  • Titre : Markov Processes with Restart
  • Résumé : We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such processes comes from modeling human and animal mobility patterns, restart processes in communication protocols, and from application of restarting random walks in information retrieval. We provide a connection between the transition probability functions of the original Markov process and the modified process with restarts. We give closed-form expressions for the invariant probability measure of the modified process. When the process evolves on the Euclidean space there is also a closed-form expression for the moments of the modified process. We show that the modified process is always positive Harris recurrent and exponentially ergodic with the index equal to (or bigger than) the rate of restarts. Finally, we illustrate the general results by the standard and geometric Brownian motions.
  • Langue du document : Anglais
  • Type de rapport : Rapport de recherche
  • Date de publication : 20/06/2012
  • Mots-clés : Markov Processes with Restart – Positive Harris Recurrence – Exponential Ergodicity – Standard and Geometric Brownian Motions
  • Référence interne : RR-8000
  • Collaboration(s) : The University of Liverpool

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  • hal-00710217, version 1
  • http://hal.inria.fr/hal-00710217
  • oai:hal.inria.fr:hal-00710217
  • Contributeur : Konstantin Avrachenkov <>
  • Soumis le : Mercredi 20 Juin 2012, 12:13:23
  • Dernière modification le : Jeudi 28 Juin 2012, 09:52:22