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Transition probability estimates for subordinate random walks

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  • Wojciech Cygan
  • Stjepan Šebek

Abstract

Let Sn be a symmetric simple random walk on the integer lattice Zd. For a Bernstein function ϕ we consider a random walk Snϕ 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 Snϕ. The main tools that we apply are a parabolic Harnack inequality and appropriate bounds for the transition kernel of the corresponding continuous time random walk.

Suggested Citation

  • Wojciech Cygan & Stjepan Šebek, 2021. "Transition probability estimates for subordinate random walks," Mathematische Nachrichten, Wiley Blackwell, vol. 294(3), pages 518-558, March.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:3:p:518-558
    DOI: 10.1002/mana.201900065
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    References listed on IDEAS

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    1. Bendikov, Alexander & Cygan, Wojciech & Trojan, Bartosz, 2017. "Limit theorems for random walks," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3268-3290.
    2. Alexander Bendikov & Wojciech Cygan, 2015. "On massive sets for subordinated random walks," Mathematische Nachrichten, Wiley Blackwell, vol. 288(8-9), pages 841-853, June.
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