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International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 443-452

Fundamental theorem of Wiener calculus

1Dept. of Math. & Stat., Miami University, Oxford, OH 45056, USA
2Dept. of Math. & Stat., University of Nebraska, Lincoln, NE 68588-0323, USA
3Dept. of Math. & Comp. Sci., Hobert & William Smith College, Geneva, NY 14456, USA

Received 12 April 1989

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we define and develop a theory of differentiation in Wiener space C[0,T]. We then proceed to establish a fundamental theorem of the integral calculus for C[0,T]. First of all, we show that the derivative of the indefinite Wiener integral exists and equals the integrand functional. Secondly, we show that certain functionals defined on C[0,T] are equal to the indefinite integral of their Wiener derivative.