Institute of Mathematics for Industry

Seminar



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Estimators based on eigenfunctions of the diffusion operator


Hold Date 2020-01-17 16:00~2020-01-17 17:00

Place Seminar Room W1-D-710, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Nicole Hufnagel (Technische Universität Dortmund)

Abstract:
Martingale estimation functions are well studied by Bibby, Sørensen (1995) and Kessler, Srensen (1999) in the case of discretely observed ergodic diffusion processes. In this talk we adapt the methodology of Kessler and Sørensen to achieve novel martingale estimation functions for a Bessel process which is a non-ergodic process. We can tackle this problem by considering a space-time transformation of the Bessel process.
We provide martingale estimation functions based on eigenfunctions of the diffusion generator for this transformed Bessel process. Following the approach of Kessler and Sørensen, consistency and asymptotic normality of these estimators can be derived. Furthermore, we compare the martingale estimation functions through a simulation study and discuss the emerging complications.