Abstract
This paper concerns the first hitting time $T_0$ of the origin for random walks on $d$-dimensional integer lattice with zero mean and a finite $2+\delta$ absolute moment ($\delta\geq0$). We derive detailed asymptotic estimates of the probabilities $\mathbb{P}_x(T_0=n)$ as $n\to\infty$ that are valid uniformly in $x$, the position at which the random walks start.
Citation
Kohei Uchiyama. "The First Hitting Time of a Single Point for Random Walks." Electron. J. Probab. 16 1960 - 2000, 2011. https://doi.org/10.1214/EJP.v16-931
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