Convergences and projection Markov property of Markov processes on ultrametric spaces

Kohei Suzuki

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Let (S, ρ) be an ultrametric space satisfying certain conditions and Sk be the quotient space of S with respect to the partition by balls with a fixed radius φ(k). We prove that, for a Hunt process X on S associated with a Dirichlet form (ε, F), a Hunt process Xk on Sk associated with the averaged Dirichlet form (εk, Fk) is Mosco convergent to X, and under certain additional conditions, Xk converges weakly to X. Moreover, we give a sufficient condition for the Markov property of X to be preserved under the canonical projection πk to Sk. In this case, we see that the projected process πk ◦ X is identical in law to Xk and converges almost surely to X.

Original languageEnglish
Pages (from-to)569-588
Number of pages20
JournalPublications of the Research Institute for Mathematical Sciences
Volume50
Issue number3
DOIs
Publication statusPublished - 2014

Keywords

  • Dirichlet forms
  • Markov functions
  • Markov processes
  • Mosco convergence
  • Projection Markov property
  • Ultrametric spaces
  • Weak convergence
  • p-adic numbers

ASJC Scopus subject areas

  • Mathematics(all)

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