Two-sided eigenvalue estimates for subordinate processes in domains |
| |
Authors: | Zhen-Qing Chen Renming Song |
| |
Affiliation: | a Department of Mathematics, University of Washington, Seattle, WA 98195, USA b Department of Mathematics, University of Illinois, Urbana, IL 61801, USA |
| |
Abstract: | Let X={Xt,t?0} be a symmetric Markov process in a state space E and D an open set of E. Denote by XD the subprocess of X killed upon leaving D. Let S={St,t?0} be a subordinator with Laplace exponent φ that is independent of X. The processes Xφ?{XSt,t?0} and are called the subordinate processes of X and XD, respectively. Under some mild conditions, we show that, if {-μn,n?1} and {-λn,n?1} denote the eigenvalues of the generators of the subprocess of Xφ killed upon leaving D and of the process XD respectively, then |
| |
Keywords: | Eigenvalues Subordination Subordinator Bernstein function Complete Bernstein function Borel right process Lé vy process Brownian motion Spherically symmetric stable process Dirichlet form Semigroup Resolvent |
本文献已被 ScienceDirect 等数据库收录! |
|