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.
- Jump-type Dirichlet form
- Stable-like process
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty