Approximation Theoretic Aspects of Probabilistic Representations for Bi-Continuous $C$-Semigroups

Abstract

By means of Riemann-Stieltjes stochastic process, moment-generating functions and operator-valued mathematical expectation, the problem of probabilistic approximation for bi-continuous $C$-semigroups is studied and the general probabilistic approximation of exponential formulas and the generation theorems are given.