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Parameter estimation for some non-recurrent solutions of SDE

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  • Dietz Hans M.
  • Kutoyants Yury A.

Abstract

The present paper deals with the problem of parameter estimation for nonlinear stochastic differential equations with solution tending to infinity with time. It is shown that if the trend coefficient is asymptotically linear (like that of an Ornstein-Uhlenbeck process), then the maximum likelihood and trajectory fitting estimators are consistent and asymptotically mixing normal. That is, these estimators behave similar as in the case of a non-ergodic Ornstein-Uhlenbeck process.

Suggested Citation

  • Dietz Hans M. & Kutoyants Yury A., 2003. "Parameter estimation for some non-recurrent solutions of SDE," Statistics & Risk Modeling, De Gruyter, vol. 21(1), pages 29-46, January.
    • Handle: RePEc:bpj:strimo:v:21:y:2003:i:1/2003:p:29-46:n:4
    DOI: 10.1524/stnd.21.1.29.20321
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    References listed on IDEAS

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    1. 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.
    2. Nakahiro Yoshida, 1990. "Asymptotic behavior of M-estimator and related random field for diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 221-251, June.
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    Cited by:

    1. Yasutaka Shimizu, 2012. "Local asymptotic mixed normality for discretely observed non-recurrent Ornstein–Uhlenbeck processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 193-211, February.
    2. Shimizu, Yasutaka, 2009. "Notes on drift estimation for certain non-recurrent diffusion processes from sampled data," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2200-2207, October.
    3. 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.
    4. Bercu, Bernard & Coutin, Laure & Savy, Nicolas, 2012. "Sharp large deviations for the non-stationary Ornstein–Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3393-3424.

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