Berry–Esseen inequalities for discretely observed diffusions

Bishwal Jaya P. N.
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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

Monte Carlo Methods and Applications, 2009, vol. 15, issue 3, 229-239

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.

Keywords: Itô stochastic differential equation; diffusion process; discrete observations; moderately increasing experimental design; approximate maximum likelihood estimators; conditional least squares estimator (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1515/MCMA.2009.013

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