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The First Hitting Time of a Single Point for Random Walks

   
@article{EJP931,
	author = {Kohei Uchiyama},
	title = {The First Hitting Time of a Single Point for Random Walks},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {16},
	year = {2011},
	keywords = {hitting time;  asymptotic expansion; Fourier analysis;  random walk},
	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.},
	pages = {no. 71, 1960-2000},
	issn = {1083-6489},
	doi = {10.1214/EJP.v16-931},    
        url = {http://ejp.ejpecp.org/article/view/931}}