On gross differentiation on Banach spaces
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
Kuo, H. (1975). On gross differentiation on Banach spaces. Pacific Journal of Mathematics, 59 (1), 135-145. https://doi.org/10.2140/pjm.1975.59.135