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Solution of jump parameter systems of differential and difference equations with semi-Markov coefficients

Part of: Equations and systems with randomness Special classes of linear operators Stochastic analysis Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Efraim Shmerling  and
Kenneth J. Hochberg
Efraim Shmerling*
Affiliation:
College of Judea and Samaria
Kenneth J. Hochberg*
Affiliation:
Bar-Ilan University
*
∗ Postal address: Department of Mathematics, College of Judea and Samaria, 44837 Ariel, Israel.
∗∗ Postal address: Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel. Email address: hochberg@macs.biu.ac.il
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Abstract

We study linear jump parameter systems of differential and difference equations whose coefficients depend on the state of a semi-Markov process. We derive systems of equations for the first two moments of the random solutions of these jump parameter systems, and illustrate how moment equations can be used in examining their asymptotic stability.

Keywords

Jump parameter systemsemi-Markov process

MSC classification

Primary: 60H25: Random operators and equations 47B80: Random operators 34F05: Equations and systems with randomness 93E03: Stochastic systems, general
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 2 , June 2003 , pp. 442 - 454
Copyright
Copyright © Applied Probability Trust 2003 

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References

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