Rates of approximation of nonsmooth integral-type functionals of Markov processes

TL;DR

This paper establishes strong $L_p$-approximation rates for nonsmooth integral functionals of Markov processes using a process-insensitive approach based on additive functional estimates.

Contribution

It introduces a novel, process-insensitive method for deriving approximation rates of nonsmooth integral functionals of Markov processes.

Findings

Provides explicit $L_p$-rates of approximation

Method applicable to a broad class of Markov processes

Enhances understanding of approximation accuracy for nonsmooth functionals

Abstract

We provide strong $L_p$-rates of approximation of nonsmooth integral-type functionals of Markov processes by integral sums. Our approach is, in a sense, process insensitive and is based on a modification of some well-developed estimates from the theory of continuous additive functionals of Markov processes.