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A Bound for the Distribution of the Hitting Time of Arbitrary Sets by Random Walk

   
@article{ECP1119,
	author = {Antal Jarai and Harry Kesten},
	title = {A Bound for the Distribution of the Hitting Time of Arbitrary Sets by Random Walk},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {9},
	year = {2004},
	keywords = {},
	abstract = {We consider a random walk $S_n = \sum_{i=1}^n X_i$ with i.i.d. $X_i$. We assume that the $X_i$ take values in $\Bbb Z^d$, have bounded support and zero mean. For $A \subset \Bbb Z^d, A \ne \emptyset$ we define $\tau_A = \inf{n \ge 0: S_n \in A}$. We prove that there exists a constant $C$, depending on the common distribution of the $X_i$ and $d$ only, such that $\sup_{\emptyset \ne A \subset \Bbb Z^d} P\{\tau_A =n\} \le C/n, n \ge 1$.},
	pages = {no. 16, 152-161},
	issn = {1083-589X},
	doi = {10.1214/ECP.v9-1119},    
        url = {http://ecp.ejpecp.org/article/view/1119}}