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 ...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 .展开更多
文摘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 .
