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

Alexander Marynych (Taras Shevchenko National University of Kiev)
Glib Verovkin (Taras Shevchenko National University of Kiev)


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).

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Pages: 1-11

Publication Date: October 31, 2014

DOI: 10.1214/ECP.v19-3641


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