Approximation-theoretic aspects of probabilistic representations for operator semigroups

AbstractIn the present paper explicit sharp estimations are provided for the rate of convergence of basically all known representation formulae for operator semigroups which in an earlier paper have been shown to arise from a single general probabilistic representation theorem based on a special version of the weak law of large numbers. As a main tool, sharp estimations for moments and moment-generating functions of suitable random variables are used. Some of the results are applied to exponential operators as well as to a class of Poisson approximation theorems in probability theory