On some smoothening effects of the transition semigroup of a Lévy process

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• 作者：Zhao Dong^a ; ^{dzhao@amt.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; Szymon Peszat^b ; ^{napeszat@cyf-kr.edu.pl" class="auth_mail" title="E-mail the corresponding author} ; Lihu Xu^c ; ^{lihuxu@umac.mo" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Bismut&ndash ; Elworthy&ndash ; Li formula ; Lé ; vy processes ; Smoothening effect
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：434
• 期：2
• 页码：1566-1580
• 全文大小：357 K

文摘

Let (P_t)$(P_t)$ be the transition semigroup of a Lévy process (L_t)$(L_t)$ taking values in a Hilbert space H. Let ν   and $\tilde{N}$ respectively be the Lévy measure and compensated Poisson random measure of (L_t)$(L_t)$. It is shown that for any bounded and measurable function f, where A_q$A_q$ is some nonlocal operator. As a corollary, As ν   can be infinite this formula establishes some smoothening effect of the semigroup (P_t)$(P_t)$. In the paper some applications of the formula will be presented as well.