Random Integral Equation of the Volterra Type with Applications

Hamdin Ahmed Alafif

Khartoum University, Faculty of Education, Omdurman, Sudan.

DOI: 10.4236/jamp.2014.25018                

Abstract

In this paper we shall present some of the most general results which have been obtained to date concerning random integral equations of the Volterra type. Some results of Tsokos [4] are given for the random integral equation; ∫ ( ) t x t w h t w k t w f x w d 0 ( ; ) = ( )+ ( ,τ ; ) τ , (τ ; ) τ (1.1) where t ≥ 0 and 1) w is appoint of Ω ; 2) h(t;w) is the stochastic free term or free random variable defined for 0 ≤ t and w ∈Ω ; 3) x(t;w) is the unknown random variable for each t ≥ 0 4) the stochastic kernel k(t,τ ;w) is defined for 0 ≤τ ≤ t < ∞ and w ∈Ω .

Keywords

Volterra Integral, Banach Space, Asymptotic Stability, Poincare-Lyapunov, Telephone Traffic Theory

Conflicts of Interest

The authors declare no conflicts of interest.

References

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