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

Part of: Inference from stochastic processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

P. E. Kloeden ,
E. Platen ,
H. Schurz  and
M. Sørensen
P. E. Kloeden*
Affiliation:
Deakin University
E. Platen*
Affiliation:
Australian National University
H. Schurz*
Affiliation:
Institute for Applied Analysis and Stochastics, Berlin
M. Sørensen*
Affiliation:
Aarhus University
*
∗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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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.

Keywords

DISCRETE TIME SAMPLINGINFERENCE FOR STOCHASTIC PROCESSESMAXIMUM LIKELIHOOD ESTIMATIONNUMERICAL METHODSSIMULATIONSTOCHASTIC DIFFERENTIAL EQUATIONSSTOCHASTIC TAYLOR EXPANSIONS

MSC classification

Primary: 65C99: None of the above, but in this section
Secondary: 62M05: Markov processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 1061 - 1076
Copyright
Copyright © Applied Probability Trust 1996 

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