Z过程上的长程陷阱模型和拟稳过程
Long range trap models on Z and quasistable processes
摘要：
设$\mathcal X=\{\mathcal X_t:\, t\geq0,\, \mathcal X_0=0\}$是$\mathbb{Z}$上具有非齐次跳跃率$\{τ_i^{-1}: i\in\mathbb{Z}\}$的平均零$β$ -稳定随机游动，其中$β\in(1,2]$和$\{τ_i: i\in\mathbb{Z}\}$是一族在$α$ -稳定律$α\in(0,1)$的吸引盆中具有共同边缘分布的独立随机变量.在本文中，我们得到的结果，这个过程的长时间的行为，特别是它的标度极限，给出了一个$β$稳定的过程的时间变化的逆的另一个过程，涉及当地的时间的$β$稳定的过程和一个独立的$α$稳定的从属，我们称由此产生的过程的准稳定的过程。另一个这样的结果与衰老有关。我们获得了$\mathcal X$的（综合）老化结果。
英文摘要：
Let $\mathcal X=\{\mathcal X_t:\, t\geq0,\, \mathcal X_0=0\}$ be a mean zero $β$-stable random walk on $\mathbb{Z}$ with inhomogeneous jump rates $\{τ_i^{-1}: i\in\mathbb{Z}\}$, with $β\in(1,2]$ and $\{τ_i: i\in\mathbb{Z}\}$ a family of independent random variables with common marginal distribution in the basin of attraction of an $α$-stable law, $α\in(0,1)$. In this paper we derive results about the long time behavior of this process, in particular its scaling limit, given by a $β$-stable process time-changed by the inverse of another process, involving the local time of the $β$-stable process and an independent $α$-stable subordinator; we call the resulting process a quasistable process. Another such result concerns aging. We obtain an (integrated) aging result for $\mathcal X$.
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