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Mean-square stability of a class of stochastic integral equations

Published online by Cambridge University Press:  17 April 2009

W.J. Padgett
W.J. Padgett
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, South Carolina, USA.
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Abstract

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The object of this paper is to investigate under very general conditions the existence and mean-square stability of a random solution of a class of stochastic integral equations in the form

for t ≥ 0, where a random solution is a second order stochastic process {x(t; w) t ≥ 0} which satisfies the equation almost certainly. A random solution x(t; w) is defined to be stable in mean-square if E[|x(t; w)|2] ≤ p for all t ≥ 0 and some p > 0 or exponentially stable in mean-square if E[|x(t; w)|2] ≤ pe-at, t ≥ 0, for some constants ρ > 0 and α > 0.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 3 , December 1972 , pp. 337 - 352
Copyright
Copyright © Australian Mathematical Society 1972

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