Random Integral Equation of the Volterra Type with Applications  

作　　者：Hamdin Ahmed Alafif 

机构地区：[1]Khartoum University, Faculty of Education, Omdurman, Sudan

出　　处：《Journal of Applied Mathematics and Physics》2014年第5期138-149,共12页应用数学与应用物理（英文）

摘　　要：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 .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 .

关 键 词：VOLTERRA Integral BANACH Space Asymptotic Stability Poincare-Lyapunov TELEPHONE Traffic Theory 

分 类 号：O1[理学—数学]