On the Height of One-Dimensional Random Walk

Mohamed Abdelkader ()
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Mohamed Abdelkader: Department of Statistics and Operations Research, Faculty of Sciences, King Saud University, Riyadh 11451, Saudi Arabia

Mathematics, 2023, vol. 11, issue 21, 1-12

Abstract: Consider the one-dimensional random walk X n : as it evolves (at each unit of time), it either increases by one with probability p or resets to 0 with probability 1 − p . In the present paper, we analyze the law of the height statistics H n , corresponding to our model X n . Also, we prove that the limiting distribution of the walk X n is a shifted geometric distribution with parameter 1 − p and find the closed forms of the mean and the variance of X n using the probability-generating function.

Keywords: height; return time; random walk (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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