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Abstract: The purpose of this note is to derive distributional properties of the random variable associated with the number of visits to state r, r 0 during the interval [0,n] of a simple random walk. The random walk is defined in the sense of Cox and Miller, allowing for three step-types, arbitrary probabilities for these steps, and arbitrary terminating state after n steps. It is also shown that some well known results can be obtained as specializations of two general Theorems. (Update)
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BibTeX entry: (Update)
@misc{ katzenbeisser-number,
author = "W. Katzenbeisser and W. Panny",
title = "On the Number of Times a Simple Random Walk Reaches a Nonnegative Height",
url = "citeseer.ist.psu.edu/596409.html" }
Citations (may not include all citations):110 The Theory of Stochastic Processes (context) - COX, MILLER - 1968
98 A System for Doing Mathematics by Computers (context) - St - 1991
65 Combinatorial Identities (context) - RIORDAN - 1968
37 Lattice Path Counting and Applications (context) - MOHANTY - 1979
9 Random Walk in Random and Non-Random Environments (context) - REVESZ - 1990
2 Green's Function Methods in Probability Theory (context) - KEILSON - 1965
2 A note on the higher moments of the random variable T associ.. (context) - KATZENBEISSER, PANNY - 1986
2 The moments of the random variable for the number of returns.. (context) - KEMP - 1987
2 Simple random walk statistics (context) - KATZENBEISSER, PANNY - 1996
1 Markovian Queuing Systems in Discrete Time (context) - OHM - 1993
1 Simple random walk and rank order statistics (context) - DWASS - 1967
1 Asymptotic results on the maximal deviation of simple random.. (context) - KATZENBEISSER, PANNY - 1984
1 discrete time analogue MM queue and transient solution geome.. (context) - PANNY, analogue et al. - 1990
1 An alternative to the KolmogorovSmirnov two-sample test (context) - KATZENBEISSER, HACKL - 1986
1 The Maximal Deviation of Lattice Paths (context) - PANNY - 1984
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