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Pseudodifferential operators and Markov processes on certain totally disconnected groups

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  • Estala-Arias, Samuel

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.

Suggested Citation

  • Estala-Arias, Samuel, 2020. "Pseudodifferential operators and Markov processes on certain totally disconnected groups," Statistics & Probability Letters, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:stapro:v:164:y:2020:i:c:s0167715220301140
    DOI: 10.1016/j.spl.2020.108811
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    References listed on IDEAS

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    1. Urban, Roman, 2012. "Markov processes on the adeles and Dedekind’s zeta function," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1583-1589.
    2. Yasuda, Kumi, 2013. "Markov processes on the adeles and Chebyshev function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 238-244.
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