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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DOI: 10.1016/j.spa.2017.08.013

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