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Stationary Distribution of Random Motion with Delay in Reflecting Boundaries
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
- 1 Tecnológico de Monterrey (ITESM), Electrical and Computer Engineering. Sucursal de correos, Monterrey, México
- 2 Tecnológico de Monterrey (ITESM), Electrical and Computer Engineering. Sucursal de correos, Monterrey, México
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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.
KeywordsRandom MotionReflecting BoundariesSemi-MarkovRandom Walk
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