Transition probability estimates for subordinate random walks

Wojciech Cygan, Stjepan Sebek

Research output: Contribution to journalArticle

Abstract

Let Sn be the simple random walk on the integer lattice Zd. For a Bernstein function Φ we consider a random walk SΦn which is subordinated to Sn. Under a certain assumption on the behaviour of Φ at zero we establish global estimates for the transition probabilities of the random walk Sn. The main tools that we apply are the parabolic Harnack inequality and appropriate bounds for the transition kernel of the corresponding continuous time random walk.
Original languageEnglish
Article numberarXiv:1812.03471v2
Number of pages34
JournalarXiv.org e-Print archive
Publication statusPublished - 25 Feb 2020

Keywords

  • Random walk
  • Discrete subordination
  • Bernstein function
  • Parabolic Harnack inequality
  • Transition probability estiamte
  • Scaling condition

ASJC Scopus subject areas

  • Mathematics(all)

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