Accuracy of discrete approximation for integral functionals of Markov processes

TL;DR

This paper investigates the convergence rates of discrete Riemann sum approximations for integral functionals of Markov processes, under certain smoothness and integrability conditions on the transition density.

Contribution

It provides new theoretical bounds on the accuracy of approximations for Markov process functionals, extending previous results to broader classes of processes.

Findings

Derived explicit convergence rate bounds for strong approximations.

Established weak approximation accuracy rates under differentiability assumptions.

Included examples illustrating the theoretical results.

Abstract

The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in $t$ and the derivative has an integrable upper bound of a certain type, we derive the accuracy rates for strong and weak approximations of the functionals by Riemannian sums. Some examples are provided.