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Weak convergence of the number of zero increments in the random walk with barrier

   
@article{ECP3641,
	author = {Alexander Marynych and Glib Verovkin},
	title = {Weak convergence of the number of zero increments in the random walk with barrier},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {random walk with barrier; recursion with random indices; renewal process; undershoot},
	abstract = {We continue the line of research of random walks with a barrier initiated by Iksanov and Möhle (2008). Assuming that the tail of the step of the underlying random walk has a power-like behavior at infinity with the exponent $-\alpha$, $\alpha\in(0,1)$, we prove that $V_n$ the number of zero increments before absoprtion in the random walk with the barrier $n$, properly centered and normalized, converges weakly to the standard normal law. Our result complements the weak law of large numbers for $V_n$ proved in Iksanov and Negadailov (2008).},
	pages = {no. 74, 1-11},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-3641},    
        url = {http://ecp.ejpecp.org/article/view/3641}}