Explosion of Jump-Type Symmetric Dirichlet Forms on ℝd

Yuichi Shiozawa, Toshihiro Uemura

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We give a sufficient condition for a class of jump-type symmetric Dirichlet forms on ℝd to be conservative in terms of the jump kernel and the associated measure. Our condition allows the coefficients dominating big jumps to be unbounded. We derive the conservativeness for Dirichlet forms related to symmetric stable processes. We also show that our criterion is sharp by using time changed Dirichlet forms. We finally remark that our approach is applicable to jump-diffusion type symmetric Dirichlet forms on ℝd.

Original languageEnglish
Pages (from-to)404-432
Number of pages29
JournalJournal of Theoretical Probability
Issue number2
Publication statusPublished - Jun 2014
Externally publishedYes


  • Conservativeness
  • Explosion
  • Jump-type Dirichlet form
  • Stable-like process

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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