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Berry–Esseen inequalities for discretely observed diffusions

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  • Bishwal Jaya P. N.

    (Department of Mathematics and Statistics, University of North Carolina at Charlotte, 376 Fretwell Bldg, 9201 University City Blvd., Charlotte, NC 28223-0001, USA. Email: J.Bishwal@uncc.edu)

Abstract

For stationary ergodic diffusions satisfying nonlinear homogeneous Itô stochastic differential equations, the paper compares the bounds on the rates of convergence to normality (Berry–Esseen type) of two approximate maximum likelihood estimators of the drift parameter based on the Itô and the Fisk–Stratonovich approximations of the continuous likelihood, under some regularity conditions, when the diffusion is observed at equally spaced dense time points over a long time interval. It shows that the Fisk–Stratonovich approximations performs better than the Itô approximations in the sense of having smaller variance.

Suggested Citation

  • Bishwal Jaya P. N., 2009. "Berry–Esseen inequalities for discretely observed diffusions," Monte Carlo Methods and Applications, De Gruyter, vol. 15(3), pages 229-239, January.
    • Handle: RePEc:bpj:mcmeap:v:15:y:2009:i:3:p:229-239:n:3
    DOI: 10.1515/MCMA.2009.013
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    References listed on IDEAS

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    1. Kasonga, R. A., 1988. "The consistency of a non-linear least squares estimator from diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 263-275, December.
    2. Shoji, Isao, 1997. "A note on asymptotic properties of the estimator derived from the Euler method for diffusion processes at discrete times," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 153-159, December.
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