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On a random solution of a nonlinear perturbed stochastic integral equation of the Volterra type

Published online by Cambridge University Press:  17 April 2009

J. Susan Milton  and
Chris P. Tsokos
J. Susan Milton
Affiliation:
Radford College, Radford, Virginia, USA
Chris P. Tsokos
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida, USA.
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Abstract

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The object of this present paper is to study a nonlinear perturbed stochastic integral equation of the form

where ω ∈ Ω, the supporting set of the complete probability measure space (Ω A, μ). We are concerned with the existence and uniqueness of a random solution to the above equation. A random solution, x(t; ω), of the above equation is defined to be a vector random variable which satisfies the equation μ almost everywhere.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 2 , October 1973 , pp. 227 - 237
Copyright
Copyright © Australian Mathematical Society 1973

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