Estimation error for occupation time functionals of stationary Markov processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Altmeyer, Randolf¹  Chorowski, Jakub¹ 

[1] Humboldt Univ, Inst Math, Unter Linden 6, D-10099 Berlin, Germany

关键词: Markov processes;    Integral functionals;    Occupation time;    Sobolev spaces;    Infinitesimal generator;    Omstein-Uhlenbeck;   

DOI  :  10.1016/j.spa.2017.08.013

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free