On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument

Henryk Gacki. "On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 16.1 (1996): 43-51. <http://eudml.org/doc/275950>.

@article{HenrykGacki1996,
abstract = {1. Introduction 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 $x(t,ω) = h(t,ω) + ∫^\{t+δ(t)\}₀ k(t,τ,ω)f(τ,x_τ(ω))dτ$, (t,ω) ∈ R⁺ × Ω, (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) xₜ(ω) denotes the restriction of the function x(t,ω) to the interval [0,t+δ(t)], t>0, with x₀(ω) = x(0,ω) ∈ L²(Ω,A,P).},
author = {Henryk Gacki},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {random integral equations with advancing argument; fixed point theorem of Darbo type},
language = {eng},
number = {1},
pages = {43-51},
title = {On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument},
url = {http://eudml.org/doc/275950},
volume = {16},
year = {1996},
}

TY - JOUR
AU - Henryk Gacki
TI - On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1996
VL - 16
IS - 1
SP - 43
EP - 51
AB - 1. Introduction 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 $x(t,ω) = h(t,ω) + ∫^{t+δ(t)}₀ k(t,τ,ω)f(τ,x_τ(ω))dτ$, (t,ω) ∈ R⁺ × Ω, (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) xₜ(ω) denotes the restriction of the function x(t,ω) to the interval [0,t+δ(t)], t>0, with x₀(ω) = x(0,ω) ∈ L²(Ω,A,P).
LA - eng
KW - random integral equations with advancing argument; fixed point theorem of Darbo type
UR - http://eudml.org/doc/275950
ER -