On purely discontinuous additive functionals of subordinate Brownian motions
主 题: On purely discontinuous additive functionals of subordinate Brownian motions
报告人: Zoran Vondracek (University of Zagreb)
时 间: 2017-07-25 16:00-17:00
地 点: 理科1号楼1303
Abstract: Let $A_t=\sum_{s\le t} F(X_{s-},X_s)$ be a purely discontinuous additive functional of a subordinate Brownian motion $X=(X_t, \P_x)$. In this talk I will describe a sufficient condition on the non-negative function $F$ that guarantees that finiteness of $A_{\infty}$ implies finiteness of its expectation. This result is then applied to study the relative entropy of $\P_x$ and the probability measure induced by a purely discontinuous Girsanov transform of the process $X$. These results are proved under the weak global scaling condition on the Laplace exponent of the underlying subordinator.
