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Parametric estimation for non recurrent diffusion processes

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  • Abi-ayad, Ilham
  • Mourid, Tahar

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.

Suggested Citation

  • Abi-ayad, Ilham & Mourid, Tahar, 2018. "Parametric estimation for non recurrent diffusion processes," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 96-102.
    • Handle: RePEc:eee:stapro:v:141:y:2018:i:c:p:96-102
    DOI: 10.1016/j.spl.2018.05.024
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    References listed on IDEAS

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    1. Yasutaka Shimizu, 2012. "Estimation of parameters for discretely observed diffusion processes with a variety of rates for information," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 545-575, June.
    2. Hans Dietz, 2001. "Asymptotic Behaviour of Trajectory Fitting Estimators for Certain Non-ergodic SDE," Statistical Inference for Stochastic Processes, Springer, vol. 4(3), pages 249-258, October.
    3. R. Höpfner & Yu. Kutoyants, 2003. "On a Problem of Statistical Inference in Null Recurrent Diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 25-42, January.
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