Multivariate Lagrange inversion and the maximum of a persistent random walk
type: Item
instance of: scholarly article
title: Multivariate Lagrange inversion and the maximum of a persistent random walk
zbMATH Open document ID: 0994.60052
DOI: 10.1016/S0378-3758(01)00149-5
author: V. Pereyra
published in: Journal of Statistical Planning and Inference
publication date: 2002-05-15T00:00:00Z
review text: Let \(\alpha \in (0,1)\) and let \(X_1, X_2, \ldots\) be the time-homogeneous Markov chain with values in \(\{+1, -1\}\) and transition probabilities given by \[ P(X_i =1\mid X_{i-1} =1) = P(X_i =-1\mid X_{i-1} =-1) = \alpha, \] \[ P(X_i =1\mid X_{i-1} =-1) = P(X_i =-1\mid X_{i-1} =1) = 1-\alpha. \] The persistent random walk \((S_n)\) is then given by \(S_n = \sum_{i=1}^n X_i\). Using multivariate Lagrange inversion, the author obtains a formula for the absorption times of this random walk which has also been derived by Mohanty (1979). He uses this result to determine the asymptotic distribution of the maximum of the persistent random walk.
reviewed by: Nina Gantert
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1741587
zbMATH Keywords: multivariate Lagrange inversion
zbMATH Keywords: correlated random walk
zbMATH Keywords: maximum of a random walk
MaRDI profile type: Publication
cites work: Q3229727
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cites work: Some explicit results for correlated random walks
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description: scientific article; zbMATH DE number 1741587