Heat content for convolution semigroups
  Let $\mathbf{X}=\{X_t\}_{t\geq 0}$ be a L\'evy process in $\mathbb{R}^d$ and $\Omega$ be an open subset of $\mathbb{R}^d$ with finite Lebesgue measure. In this article we consider the quantity $H (t) = \int_{\Omega}\mathbb{P}_{x} (X_t\in \Omega ^c) dx$ which is called the heat content. We study its asymptotic behaviour as $t$ goes to zero for isotropic L\'evy processes under some mild assumptions on the characteristic exponent. We also treat the class of L\'evy processes with finite variation in full generality. 
Wojciech Cygan, Tomasz Grzywny
math.PR