演講者：陳振慶教授
單 位：University of Washington
日 期：2011年8月10日 AM 11:00
地 點：國立高雄大學理學院408室
講 題：Uniform integrability of exponential martingales and spectral bounds of Feynman-Kac semigroups
摘 要：
In the first part of this talk, I will present a useful criterion for uniform integrability of exponential martingales in the context of Markov processes. The condition of this criterion is easy to verify and is, in general, much weaker than the commonly used Novikov's condition. In the second part of this talk, I will present a new approach to the study of spectral bounds of Feynman-Kac semigroups for a large class of symmetric Markov processes. We first establish criteria for the Lp -independence of spectral bounds for Feynman-Kac semigroups generated by continuous additive functionals, using gaugeability results for Feynman-Kac functionals. We then extend these analytic criteria for the Lp -independence of spectral bounds to non-local Feynman-Kac semigroups via pure jump Girsanov transforms. For this, the uniform integrability result of the exponential martingales in the first part of this talk will play an important role. We use it to show that appropriate Kato classes can only become larger under pure jump Girsanov transforms with symmetric jumping functions.
