**Vassili N. Kolokoltsov**

*Article*

Department of Statistics, University of Warwick, Coventry CV4 7AL, UK; v.kolokoltsov@warwick.ac.uk

Received: 28 February 2020; Accepted: 30 March 2020; Published: 1 April 2020

**Abstract:** We obtained the exact estimates for the error terms in Laplace's integrals and sums implying the corresponding estimates for the related laws of large number and central limit theorems including the large deviations approximation.

**Keywords:** integrals and sums; rates of convergence; conditional law of large numbers; conditional central limit theorem
