Transition probability estimates for subordinate random walks

Wojciech Cygan and Stjepan Šebek

Mathematische Nachrichten, 2021, vol. 294, issue 3, 518-558

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.

Date: 2021
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https://doi.org/10.1002/mana.201900065

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