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The Equations of Markovian Random Evolution on the Line

Part of:Special processesMarkov processes

Published online by Cambridge University Press:  14 July 2016

Alexander Kolesnik
Alexander Kolesnik*
Affiliation:
Institute of Mathematics, Kishinev
*
∗ Postal address: Institute of Mathematics, Academy Street 5, Kishinev 277028, Moldova. e-mail address: 16kolesn@mathem.moldova.su
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Abstract

We consider a general model of one-dimensional random evolution with n velocities and rates of a switching Poisson process (n ≥ 2). A governing nth-order hyperbolic equation in a determinant form is given. For two important particular cases it is written in an explicit form. Some known hyperbolic equations are obtained as particular cases of the general model

Keywords

Random evolutionsrandom motionshigh-order hyperbolic equations

MSC classification

Primary:60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary:60J60: Diffusion processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998, pp. 27 - 35
Copyright
Copyright © Applied Probability Trust 1998 

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