# Estimation error for occupation time functionals of stationary Markov processes

*Randolf Altmeyer* and
*Jakub Chorowski*

*Stochastic Processes and their Applications*, 2018, vol. 128, issue 6, 1830-1848

**Abstract:**
The approximation of integral functionals with respect to a stationary Markov process by a Riemann sum estimator is studied. Stationarity and the functional calculus of the infinitesimal generator of the process are used to explicitly calculate the estimation error and to prove a general finite sample error bound. The presented approach admits general integrands and gives a unifying explanation for different rates obtained in the literature. Several examples demonstrate how the general bound can be related to well-known function spaces.

**Keywords:** Markov processes; Integral functionals; Occupation time; Sobolev spaces; Infinitesimal generator; Ornstein–Uhlenbeck (search for similar items in EconPapers)

**Date:** 2018

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