Heat content for convolution semigroups

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• 作者：Wojciech Cygan^a ; ¹ ; ^{wojciech.cygan@uwr.edu.pl" class="auth_mail" title="E-mail the corresponding author} ; Tomasz Grzywny^b ; ² ; ^{tomasz.grzywny@pwr.edu.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Asymptotic behaviour ; Characteristic exponent ; Heat content ; Isotropic Lé ; vy process ; Perimeter ; Regular variation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1393-1414
• 全文大小：432 K

文摘

Let X={X_t}_t≥0$\mathbf{X}={\{X_t\}}_{t\ge 0}$ be a Lévy process in R^d${\mathbb{R}}^d$ and Ω be an open subset of R^d${\mathbb{R}}^d$ with finite Lebesgue measure. In this article we consider the quantity $H(t)={\int }_{\mathrm{\Omega }}{\mathbb{P}}_x(X_t\in {\mathrm{\Omega }}^c)\mathrm{d}x$ related to X which is called the heat content. We study its asymptotic behaviour as t goes to zero for isotropic Lévy processes under some mild assumptions on the characteristic exponent. We also treat the class of Lévy processes with finite variation in full generality.