Stationary Distribution of Random Motion with Delay in Reflecting Boundaries

Anatoliy A. Pogorui, Ramón M. Rodríguez-Dagnino

Tecnológico de Monterrey (ITESM), Electrical and Computer Engineering. Sucursal de correos, Monterrey, México.

DOI: 10.4236/am.2010.11004                

Abstract

In this paper we study a continuous time random walk in the line with two boundaries [a,b], a < b. The particle can move in any of two directions with different velocities v1 and v2. We consider a special type of boundary which can trap the particle for a random time. We found closed-form expressions for the stationary distribution of the position of the particle not only for the alternating Markov process but also for a broad class of semi-Markov processes.

Keywords

Random Motion, Reflecting Boundaries, Semi-Markov, Random Walk

Conflicts of Interest

The authors declare no conflicts of interest.

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