arXiv · 1209.1761
On the Escape of a Random Walk From Two Pieces of a Tripartite Set
Abstract
Let $\{A, B, C\}$ be a partition of a sample space $Ω$. For a random walk $S_n = x + \sum_{j=1}^n X_j$ starting at $x \in A$, we find estimates for the Green's function $G_{A \cup B}(x,y)$ and the hitting time $E^x(T_C)$ for $x, y \in A \cup B$, with interest in the case where $C$ "separates" $A$ and $B$ in a sense (e.g. the probability of jumping from $A$ to $B$, or vice versa, before hitting $C$, is small).
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Michael Carlisle. 2014-05-14. On the Escape of a Random Walk From Two Pieces of a Tripartite Set. https://arxiv.org/abs/1209.1761
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