Random Integral Equation of the Volterra Type with Applications

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Author(s)  

Hamdin Ahmed Alafif

Affiliation(s)

Khartoum University, Faculty of Education, Omdurman, Sudan.

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

Cite this paper

Alafif, H. (2014) Random Integral Equation of the Volterra Type with Applications. Journal of Applied Mathematics and Physics, 2, 138-149. doi: 10.4236/jamp.2014.25018.

 

References

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