Estimation error for occupation time functionals of stationary Markov processes
Probability
2016-10-18 v1 Statistics Theory
Statistics Theory
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 get a better understanding of the estimation error and to prove a general 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.
Cite
@article{arxiv.1610.05225,
title = {Estimation error for occupation time functionals of stationary Markov processes},
author = {Randolf Altmeyer and Jakub Chorowski},
journal= {arXiv preprint arXiv:1610.05225},
year = {2016}
}