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In this paper we evaluate the conditional Yeh-Wiener integral E(F(x)|x(s,t)=ζ) for functions F of the form F(x)=exp{∫ 0 t ∫ 0 s o(σ,τ,x(σ,τ))dσdτ}. The method we use to evaluate this conditional integral is to first define a sample path-valued conditional Yeh-Wiener integral of the type E(F(x)|x(s,.)=ψ(.)) and show that it satisfies a Wiener integral equation. We next obtain a series solution for E(F(x)|x(s,.)=ψ(.)) by solving this Wiener integral equation. Finally, we integrate this series solution appropriately in order to evaluate E(F(x)|x(s,t)=ζ)

Sample path-valued conditional Yeh-Wiener integrals and a Wiener integral equation