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Exponential Moments of First Passage Times and Related Quantities for Random Walks

   
@article{ECP1569,
	author = {Alexander Iksanov and Matthias Meiners},
	title = {Exponential Moments of First Passage Times and Related Quantities for Random Walks},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {15},
	year = {2010},
	keywords = {first-passage time, last exit time, number of visits, random walk, renewal theory},
	abstract = {For a zero-delayed random walk on the real line, let $τ(x)$, $N(x)$ and $ρ(x)$ denote the first passage time into the interval $(x,∞)$, the number of visits to the interval $(-∞,x]$ and the last exit time from $(-∞,x]$, respectively. In the present paper, we provide ultimate criteria for the finiteness of exponential moments of these quantities. Moreover, whenever these moments are finite, we derive their asymptotic behaviour, as $x → ∞$.},
	pages = {no. 34, 365-375},
	issn = {1083-589X},
	doi = {10.1214/ECP.v15-1569},    
        url = {http://ecp.ejpecp.org/article/view/1569}}