Sample path-valued conditional Yeh-Wiener integrals and a Wiener integral equation
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- by Chull Park and David Skoug PDF
- Proc. Amer. Math. Soc. 115 (1992), 479-487 Request permission
Abstract:
In this paper we evaluate the conditional Yeh-Wiener integral $E(F(x)|x(s,t) = \xi )$ for functions $F$ of the form \[ F(x) = \exp \{ \int _0^t {\int _0^s \phi } (\sigma ,\tau ,x(\sigma ,\tau ))d\sigma d\tau \} .\] The method we use to evaluate this conditional integral is to first define a sample path-valued conditional Yeh-Wiener integral of the type $E(F(x)|x(s,) = \psi ())$ and show that it satisfies a Wiener integral equation. We next obtain a series solution for $E(F(x)|x(s,) = \psi ())$ by solving this Wiener integral equation. Finally, we integrate this series solution appropriately in order to evaluate $E(F(x)|x(s,t) = \xi )$.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 479-487
- MSC: Primary 28C20; Secondary 60J65
- DOI: https://doi.org/10.1090/S0002-9939-1992-1104401-3
- MathSciNet review: 1104401