Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Conditional Yeh-Wiener integrals with vector-valued conditioning functions


Authors: Chull Park and David Skoug
Journal: Proc. Amer. Math. Soc. 105 (1989), 450-461
MSC: Primary 60J65; Secondary 28C20
MathSciNet review: 960650
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Abstract: In this paper we establish various results involving conditional Yeh-Wiener integrals with vector-valued conditioning functions. We first develop a very simple formula for converting conditional Yeh-Wiener integrals into ordinary (i.e., nonconditional) Yeh-Wiener integrals. We then use this simple formula to evaluate the conditional Yeh-Wiener integral of various functionals, including functionals in which the sectional average of an $ {L_2}$-function occurs naturally. Finally, we use these results to obtain a general Cameron-Martin type translation theorem for conditional Yeh-Wiener integrals.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0960650-6
Keywords: Yeh-Wiener integral, conditional Yeh-Wiener integral, Cameron-Martin translation theorem
Article copyright: © Copyright 1989 American Mathematical Society