International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 443-452
doi:10.1155/S0161171290000667
Fundamental theorem of Wiener calculus
Chull Park1
, David Skoug2
and Lawrence Smolowitz3
1Dept. of Math. \& Stat., Miami University, Oxford 45056, OH, USA
2Dept. of Math. \& Stat., University of Nebraska, Lincoln 68588-0323, NE, USA
3Dept. of Math. \& Comp. Sci., Hobert \& William Smith College, Geneva 14456, NY, USA
Abstract
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.