Transition probability estimates for subordinate random walks

Wojciech Cygan, Stjepan Sebek

Research output: Contribution to journalArticleResearchpeer-review

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
Number of pages34
JournalarXiv.org e-Print archive
Publication statusSubmitted - 2019

Fingerprint

Transition Probability
Random walk
Bernstein Function
Continuous Time Random Walk
Harnack Inequality
Simple Random Walk
Estimate
kernel
Integer
Zero

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Cygan, W., & Sebek, S. (2019). Transition probability estimates for subordinate random walks. Manuscript submitted for publication.

Transition probability estimates for subordinate random walks. / Cygan, Wojciech; Sebek, Stjepan.

In: arXiv.org e-Print archive, 2019.

Research output: Contribution to journalArticleResearchpeer-review

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