This article is cited in 3 papers

Oscillating Random Walks with Two Levels of Switching

D. K. Kim^a, V. I. Lotov<sup>b

a</sup> Novosibirsk State University, Mechanics and Mathematics Department
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We consider a Markov random walk $X_n$, $n\ge 0$, generated by the sums of independent random variables. Each successive jump of the random walk is distributed in accord with one of three laws in dependence on the location of a walking particle: within some interval $[a,b]$, to the left of the point $a$, or to the right of the point $b$. Using factorization methods, we obtain some representations for the double Laplace–Stieltjes transforms (in time and spatial variables) of the distribution of $X_n$ and find the transforms of the stationary distribution of a chain.

Key words: oscillating random walk, stationary distribution, factorization identities.

UDC: 519.21

Received: 02.04.2002

 English version: Siberian Advances in Mathematics, 2004, 14:1, 7–46

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