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On LAN for parametrized continuous periodic signals in a time inhomogeneous diffusion

Author

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  • Höpfner Reinhard
  • Kutoyants Yury A.

    (Université du Maine, Laboratoire de Statistique et Processus, Le Mans cedex 9, Frankreich)

Abstract

We consider a diffusion (ξt)t≥0 whose drift involves some T-periodic signal. T is fixed and known, whereas the signal depends on a d-dimensional parameter θ∈Θ. Assuming positive Harris recurrence of the grid chain (ξkT)k∈N0 and exploiting the periodic structure in the semigroup, we work with path segments and limit theorems for certain functionals (more general than additive functionals) of the process to prove local asymptotic normality (LAN). Then we consider several estimators for the unknown parameter.

Suggested Citation

  • Höpfner Reinhard & Kutoyants Yury A., 2009. "On LAN for parametrized continuous periodic signals in a time inhomogeneous diffusion," Statistics & Risk Modeling, De Gruyter, vol. 27(4), pages 309-326, December.
    • Handle: RePEc:bpj:strimo:v:27:y:2009:i:4:p:309-326:n:5
    DOI: 10.1524/stnd.2009.1064
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    References listed on IDEAS

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    1. Cremers, Heinz & Kadelka, Dieter, 1986. "On weak convergence of integral functionals of stochastic processes with applications to processes taking paths in LEP," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 305-317, February.
    2. Herold Dehling & Brice Franke & Thomas Kott, 2010. "Drift estimation for a periodic mean reversion process," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 175-192, October.
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