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Estimation error for occupation time functionals of stationary Markov processes

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  • Altmeyer, Randolf
  • Chorowski, Jakub

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.

Suggested Citation

  • Altmeyer, Randolf & Chorowski, Jakub, 2018. "Estimation error for occupation time functionals of stationary Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1830-1848.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:6:p:1830-1848
    DOI: 10.1016/j.spa.2017.08.013
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
    2. Kohatsu-Higa, A. & Makhlouf, A. & Ngo, H.L., 2014. "Approximations of non-smooth integral type functionals of one dimensional diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1881-1909.
    3. Catellier, R. & Gubinelli, M., 2016. "Averaging along irregular curves and regularisation of ODEs," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2323-2366.
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