Discussiones Mathematicae Differential Inclusions 16(1) (1996) 4351
Henryk Gacki
Institute of Mathematics, Silesian University
40007 Katowice, Poland
Random Integral Equations play a significant role in characterizing of many biological and engineering problems [4,5,6,7].
We present here new existence theorems for a class of integral equations with advancing argument. Our method is based on the notion of a measure of noncompactness in Banach spaces and the fixed point theorem of Darbo type. We shall deal with random integral equation with advancing argument

(1) 
where
(i)  (Ω, A,P) is a complete probability space, 
(ii)  x = x(t,ω) denotes an unknown random function defined for t ∈ R^{+} and ω ∈ Ω, 
(iii)  δ is a nonnegative function from R^{+} into R^{+}, 
(iv)  x_{t}(ω) denotes the restriction of the function x(t,ω) to the interval [0,t+δ(t)], t>0, with x_{0}(ω) = x(0,ω) ∈ L^{2}(Ω, A,P). 
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