Weak convergence of the number of zero increments in the random walk with barrier
Abstract
We continue the line of research of random walks with barrier initiated by Iksanov and M{ö}hle (2008). Assuming that the tail of the step of the underlying random walk has a powerlike behavior at infinity with exponent $\alpha$, $\alpha\in(0,1)$, we prove that the number $V_n$ of zero increments in the random walk with barrier, properly centered and normalized, converges weakly to the standard normal law. This refines previously known weak law of large numbers for $V_n$ proved in Iksanov and Negadailov (2008).
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 DOI:
 10.48550/arXiv.1407.1186
 arXiv:
 arXiv:1407.1186
 Bibcode:
 2014arXiv1407.1186M
 Keywords:

 Mathematics  Probability;
 60C05;
 60G09
 EPrint:
 12 pages