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Transition probability estimates for subordinate random walks
Author(s) -
Cygan Wojciech,
Šebek Stjepan
Publication year - 2021
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900065
Subject(s) - random walk , mathematics , simple random sample , integer lattice , heterogeneous random walk in one dimension , transition (genetics) , harnack's inequality , lattice (music) , statistical physics , combinatorics , discrete mathematics , pure mathematics , statistics , half integer , biochemistry , chemistry , gene , population , physics , demography , quantum mechanics , sociology , acoustics
Abstract Let S n be a symmetric simple random walk on the integer lattice Z d . For a Bernstein function ϕ we consider a random walk S n ϕ which is subordinated to S n . Under a certain assumption on the behaviour of ϕ at zero we establish global estimates for the transition probabilities of the random walk S n ϕ . 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.