On general perturbations of symmetric Markov processes |
| |
| Authors: | Z-Q Chen PJ Fitzsimmons K Kuwae T-S Zhang |
| |
| Institution: | aDepartment of Mathematics, University of Washington, Seattle, WA 98195, USA;bDepartment of Mathematics, University of California at San Diego, La Jolla, CA 92093-0112, USA;cDepartment of Mathematics and Engineering, Graduate School of Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan;dSchool of Mathematics, University of Manchester, Sackville Street, Manchester M60 1QD, UK |
| |
| Abstract: | Let X be a symmetric right process, and let  be a multiplicative functional of X that is the product of a Girsanov transform, a Girsanov transform under time-reversal and a continuous Feynman–Kac transform. In this paper we derive necessary and sufficient conditions for the strong L2-continuity of the semigroup  given by Ttf(x)=ExZtf(Xt)], expressed in terms of the quadratic form obtained by perturbing the Dirichlet form of X in the appropriate way. The transformations induced by such Z include all those treated previously in the literature, such as Girsanov transforms, continuous and discontinuous Feynman–Kac transforms, and generalized Feynman–Kac transforms. |
| |
| Keywords: | Dirichlet form Perturbation Symmetric Markov process Time reversal |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
