论文标题
在随机风景中自我归一化随机行走的中等偏差
Moderate deviations for the self-normalized random walk in random scenery
论文作者
论文摘要
让$ g $是带顶点套装$ v $的无限连接图。令$ \ {s_n：n \ in \ mathbb n_0 \} $为$ g $上的简单随机步行，让$ \ {ξ（v）：v \ in v \} $是i.i.d的集合。独立于随机步行的随机变量。在随机风景中定义随机步行为$ t_n = \ sum_ {k = 0}^nξ（s_k）$，而归一化变量$ v_n =（\ sum_ {k = 0}^nξ^2（s_k） \ ell^2_n（v））^{1/2} $。对于$ g = \ mathbb z^d $和$ g = \ mathbb t_d $，$ d $ -ary树，我们为自级化的过程提供较大的偏差结果$ t_n \ sqrt {n}/（l_ {l_ {n，2} v_n）在场景上仅在有限的有限矩假设下。
Let $G$ be an infinite connected graph with vertex set $V$. Let $\{S_n: n \in \mathbb N_0 \}$ be the simple random walk on $G$ and let $\{ ξ(v) : v \in V \}$ be a collection of i.i.d. random variables which are independent of the random walk. Define the random walk in random scenery as $T_n = \sum_{k=0}^n ξ(S_k)$, and the normalization variables $V_n = (\sum_{k=0}^n ξ^2(S_k))^{1/2}$ and $L_{n,2} = (\sum_{v \in V} \ell^2_n(v))^{1/2}$. For $G= \mathbb Z^d$ and $G = \mathbb T_d$, the $d$-ary tree, we provide large deviations results for the self-normalized process $T_n \sqrt{n}/(L_{n,2}V_n)$ under only finite moment assumptions on the scenery.
