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Derivative of the Donsker delta functionals. (English) Zbl 1474.28022

Summary: We prove that derivatives of any finite order of Donsker’s delta functionals are well-defined elements in the space of Hida distributions. We also show the convergence to the derivative of Donsker’s delta functionals of two different approximations. Finally, we present an existence result of finite product and infinite series of the derivative of the Donsker delta functionals.

MSC:

28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
46F25 Distributions on infinite-dimensional spaces
60G20 Generalized stochastic processes
60H40 White noise theory
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