Pseudodifferential operators and Markov processes on certain totally disconnected groups

Samuel Estala-Arias

Statistics & Probability Letters, 2020, vol. 164, issue C

Abstract: This article describes a class of invariant Markov processes on certain totally disconnected groups. An invariant pseudodifferential operator on these groups, similar to the Vladimirov operator on the p-adic line, allows us to state an L2-abstract Cauchy problem for a homogeneous heat-type pseudodifferential equation. The fundamental solutions of these parabolic-type pseudodifferential equations give transition functions of time and space homogeneous Markov processes on these groups. Particularly interesting examples are polyadic rings, such as the ring of m-adic numbers, and the ring of finite adèles of the rational numbers.

Keywords: Totally disconnected groups; Ultrametrics; Pseudodifferential operators; Markov processes (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108811

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