Stationary Distribution of Random Motion with Delay in Reflecting Boundaries

Affiliation(s)

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

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

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.

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.

Cite this paper

nullA. Pogorui and R. Rodríguez-Dagnino, "Stationary Distribution of Random Motion with Delay in Reflecting Boundaries,"*Applied Mathematics*, Vol. 1 No. 1, 2010, pp. 24-28. doi: 10.4236/am.2010.11004.

nullA. Pogorui and R. Rodríguez-Dagnino, "Stationary Distribution of Random Motion with Delay in Reflecting Boundaries,"

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