Rate of convergence in Trotter's approximation theorem and its applications

TL;DR

This paper establishes a new, general rate of convergence in Trotter's approximation theorem and demonstrates its effectiveness in deriving quantitative estimates for limit theorems in probability theory.

Contribution

It provides a comprehensive rate of convergence in Trotter's theorem applicable in full generality, enhancing the theorem's practical utility.

Findings

New rate of convergence in Trotter's theorem established

Application to quantitative estimates in probability limit theorems

Improves understanding of operator semigroup approximations

Abstract

The celebrated Trotter approximation theorem provides a sufficient condition for the convergence of a sequence of operator semigroups in terms of the corresponding sequence of infinitesimal generators. There exist a few results on the rate of convergence in Trotter's theorem under some constraints. In the present paper, a new rate of convergence in Trotter's theorem in full generality is given. Moreover, we see that this rate of convergence works well to obtain quantitative estimates for some limit theorems in probability theory.