论文标题
与泊松场相互作用的对称莱维过程的淬火渐近学
Quenched asymptotics for symmetric Lévy processes interacting with Poissonian fields
论文作者
论文摘要
我们为普通泊松潜力中的纯跳跃对称莱维过程建立了明确的淬火渐近学，这与泊松互动的非局部抛物线安德森问题的解决方案的较大时间渐近行为密切相关。特别是，当密度相对于相关Lévy度量的LEBESGUE度量函数时，由$$ρ（z）= \ frac {1} {| z | | | |^{d+α}}} \ i _ {\ i _ {\ {| z | | | | \ le 1 \}}}}+ e^{ - 1 \}} $$对于某些$α\（0,2）$，$θ\ in（0，\ infty] $和$ c> 0 $，精确淬火的渐近分数是针对由$φ（x）= 1 \ wedge | x | x | x | x | x | for的$φ（x）给出的形状功能的潜在的（ 2 $。
We establish explicit quenched asymptotics for pure-jump symmetric Lévy processes in general Poissonian potentials, which is closely related to large time asymptotic behavior of solutions to the nonlocal parabolic Anderson problem with Poissonian interaction. In particular, when the density function with respect to the Lebesgue measure of the associated Lévy measure is given by $$ρ(z)= \frac{1}{|z|^{d+α}}\I_{\{|z|\le 1\}}+ e^{-c|z|^θ}\I_{\{|z|> 1\}}$$ for some $α\in (0,2)$, $θ\in (0,\infty]$ and $c>0$, exact quenched asymptotics is derived for potentials with the shape function given by $φ(x)=1\wedge |x|^{-d-β}$ for $β\in (0,\infty]$ with $β\neq 2$. We also discuss quenched asymptotics in the critical case (e.g.,\, $β=2$ in the example mentioned above).
