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Fortet, R. (1956) Random Distributions with Application to Telephone Engineering. Proc. Berkeley Symp. Math. Statist and Probability, 3rd, 11, 81-88.

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• TITLE: Random Integral Equation of the Volterra Type with Applications

  AUTHORS: Hamdin Ahmed Alafif

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.5, April 25, 2014

  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