Perturbation of dirichlet forms and stability of fundamental solutions

Masaki Wada

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let {Xt}t≥0 be the α-stable-like or relativislic α-stable-like process on ℝd generated by a certain symmetric jump-type regular Dirichlet form (ε,F). It is known in [5,7] that the transition probability density p(t,x,y) of {Xt}t≥0 admits the two-sided estimates. Let μ be a positive smooth Radon measure in a certain class and consider the perturbed form εμ(u,u) = ε(u,u) - (u,u)μ. Denote by pμ(t,x,y) the fundamental solution associated with εμ. In this paper, we establish a necessary and sufficient condition on μ for pμ(t. x, y) having the same two-sided estimates as p(t, x, y) up to positive constants.

Original languageEnglish
Pages (from-to)523-537
Number of pages15
JournalTohoku Mathematical Journal
Volume66
DOIs
Publication statusPublished - 2014 Dec

Keywords

  • Dirichlet forms
  • Heat kernel
  • Markov processes
  • Perturbation

ASJC Scopus subject areas

  • Mathematics(all)

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