Continuous essential selections and integral functionals

GENERALIZED POSITIVE DEFINITE FUNCTIONS AND COMPLETELY MONOTONE FUNCTIONS ON FOUNDATION SEMIGROUPS

A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...

Two Types of RG-Factorizations of Continuous-Time Level-Dependent Quasi-Birth-and-Death Processes and Their Applications to Stochastic Integral Functionals

In this paper, we provide UL-type and LU -type RG-factorizations for an irreducible continuous-time level-dependent quasi-birth-and-death (QBD) process with either finitely-many levels or infinitely-many levels, and then apply theRG-factorizations to solve a type of linear QBD-equations, which is always crucial for analyzing a stochastic model described as a QBD process. Based on the results ob...

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Integral Representation of Continuous Comonotonically Additive Functionals

In this paper, I first prove an integral representation theorem: Every quasi-integral on a Stone lattice can be represented by a unique uppercontinuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinite...

Integral transforms, convolution products, and first variations

We establish the various relationships that exist among the integral transform Ᏺ α,β F , the convolution product (F * G) α , and the first variation δF for a class of functionals defined on K[0,T ], the space of complex-valued continuous functions on [0,T ] which vanish at zero. 1. Introduction and definitions. In a unifying paper [10], Lee defined an integral transform Ᏺ α,β of analytic functi...