Martingale estimation functions for Bessel processes

Nicole Hufnagel () and Jeannette H. C. Woerner ()
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Nicole Hufnagel: Technische Universität Dortmund
Jeannette H. C. Woerner: Technische Universität Dortmund

Statistical Inference for Stochastic Processes, 2022, vol. 25, issue 2, No 5, 337-353

Abstract: Abstract In this paper we derive martingale estimating functions for the dimensionality parameter of a Bessel process based on the eigenfunctions of the diffusion operator. Since a Bessel process is non-ergodic and the theory of martingale estimating functions is developed for ergodic diffusions, we use the space-time transformation of the Bessel process and formulate our results for a modified Bessel process. We deduce consistency, asymptotic normality and discuss optimality. It turns out that the martingale estimating function based of the first eigenfunction of the modified Bessel process coincides with the linear martingale estimating function for the Cox Ingersoll Ross process. Furthermore, our results may also be applied to estimating the multiplicity parameter of a one-dimensional Dunkl process and some related polynomial processes.

Keywords: Bessel process; Non-ergodic diffusion; Martingale estimating function; Eigenfunctions; Primary 62M15; Secondary 60J60 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11203-021-09250-8

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