Parametric estimation for non recurrent diffusion processes

Ilham Abi-ayad and Tahar Mourid

Statistics & Probability Letters, 2018, vol. 141, issue C, 96-102

Abstract: We consider the trajectory fitting estimators (TFEs) of a parameter in the drift coefficient of a non-recurrent diffusion processes introduced by Keller et al. (1984). We show the strong consistence and Gaussian limit distribution of the TFEs when one continuously observes a sample path over a time interval and obtain rate of convergence greater-order than the standard case. These results extend Dietz (2001) and Dietz and Kutoyants (2003) results in linear and polynomial cases. Numerical simulations illustrate the behavior of the estimators.

Keywords: Diffusion processes; Non-recurrence; Fitting trajectory estimators; Strong consistency; Asymptotic law (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.05.024

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