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Explosion of Jump-Type Symmetric Dirichlet Forms on ℝd

Research paper by Yuichi Shiozawa, Toshihiro Uemura

Indexed on: 30 May '12Published on: 30 May '12Published in: Journal of Theoretical Probability



Abstract

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.