Spectral Integrals of Bernoulli Generalized Functionals

Abstract

Let $\mathcal{S}\subset {\mathcal{L}}^2\subset {\mathcal{S}}^{\ast }$ be the Gel'fand triple over the Bernoulli space, where elements of ${\mathcal{S}}^{\ast }$ are called Bernoulli generalized functionals. In this paper, we define integrals of Bernoulli generalized functionals with respect to a spectral measure (projection operator-valued measure) in the framework of $\mathcal{S}\subset {\mathcal{L}}^2\subset {\mathcal{S}}^{\ast }$, and examine their fundamental properties. New notions are introduced, several results are obtained and examples are also shown.

This article has been accepted by the journal [Stochastics: An International Journal of Probability and Stochastic Processes]

References in corpus (1)

• Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals