Document Type

Article

Publication Date

1-1-1975

Abstract

Let Pt (x, ·) denote the Wiener measure in an abstract Wiener space (H, B) with variance parameter t > 0 and mean x in B. It is shown that if [FORMULA PRESENTED]; 0 and x are fixed, then the function ptf defined by [FORMULA PRESENTED] for h in H is infinitely Gross differentiable at x. The first two derivatives are given by [FORMULA PRESENTED], where h and k are in H. Moreover, [FORMULA PRESENTED] is a Hilbert-Schmidt operator and [FORMULA PRESENTED]. An application to Uhlenbeck- Ornstein process is also given. © 1975 Pacific Journal of Mathematics.

Publication Source (Journal or Book title)

Pacific Journal of Mathematics

First Page

135

Last Page

145

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