论文标题
非局部热含量的渐近扩张
Asymptotic expansion of the nonlocal heat content
论文作者
论文摘要
令$ \ {x} = \ {x_t \} _ {t \ geq 0} $是$ \ m athbb {r}^d $和$ω$的lévy进程，是$ \ mathbb {r mathbb {r} d $ with Foriite lebesgue测度。在本文中，我们考虑数量$ h（t）= \int_Ω\ mathbb {p}^x（x_t \inΩ^c）\，\ mathrm {d} x $，称为热含量。我们研究了其对特征指数的轻度假设，其对各向同性$α$稳定的莱维过程和更通用的莱维过程的渐近扩展。
Let $\mathbf{X}=\{X_t\}_{t\geq 0}$ be a Lévy process in $\mathbb{R}^d$ and $Ω$ be an open subset of $\mathbb{R}^d$ with finite Lebesgue measure. In this article we consider the quantity $H(t)=\int_Ω \mathbb{P}^x (X_t\inΩ^c) \, \mathrm{d}x$ which is called the heat content. We study its asymptotic expansion for isotropic $α$-stable Lévy processes and more general Lévy processes, under mild assumptions on the characteristic exponent.
