Approximation Theoretic Aspects of Probabilistic Representations for Bi-Continuous $C$-Semigroups (Communications in Mathematical Research, 2021)
By means of Riemann-Stieltjes stochastic process, moment-generatingfunctions and operator-valued mathematical expectation, the problem of probabilisticapproximation for bi-continuous $C$-semigroups is studied and the general probabilisticapproximation of exponential formulas and the generation theorems are given.
Keywords: bi-continuous $C$-semigroup; probabilistic approximation; generation theorem.