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Central limit theorems for discretized occupation time functionals

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  • Altmeyer, Randolf

Abstract

The approximation of integral type functionals is studied for discrete observations of a continuous Itô semimartingale. Based on novel approximations in the Fourier domain, central limit theorems are proved for L2-Sobolev functions with fractional smoothness. An explicit L2(P)-lower bound shows that already lower order quadrature rules, such as the trapezoidal rule and the classical Riemann estimator, are rate optimal, but only the trapezoidal rule is efficient, achieving the minimal asymptotic variance.

Suggested Citation

  • Altmeyer, Randolf, 2023. "Central limit theorems for discretized occupation time functionals," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 101-125.
    • Handle: RePEc:eee:spapps:v:156:y:2023:i:c:p:101-125
    DOI: 10.1016/j.spa.2022.11.006
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    References listed on IDEAS

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    1. Jacod, Jean & Mykland, Per A., 2015. "Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2910-2936.
    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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