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On effects of discretization on estimators of drift parameters for diffusion processes

  • P. E. Kloeden (a1), E. Platen (a2), H. Schurz (a3) and M. Sørensen (a4)

Abstract

In this paper statistical properties of estimators of drift parameters for diffusion processes are studied by modern numerical methods for stochastic differential equations. This is a particularly useful method for discrete time samples, where estimators can be constructed by making discrete time approximations to the stochastic integrals appearing in the maximum likelihood estimators for continuously observed diffusions. A review is given of the necessary theory for parameter estimation for diffusion processes and for simulation of diffusion processes. Three examples are studied.

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Corresponding author

Postal address: School of Computing and Mathematics, Deakin University, Geelong, Victoria 3217, Australia.
∗∗ Postal address: Centre for Financial Mathematics, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia.
∗∗∗ Postal address: Institute for Applied Analysis and Stochastics, Berlin, Germany.
∗∗∗∗ Postal address: Department of Theoretical Statistics, Institute of Mathematics, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark.

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On effects of discretization on estimators of drift parameters for diffusion processes

  • P. E. Kloeden (a1), E. Platen (a2), H. Schurz (a3) and M. Sørensen (a4)

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