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

Höpfner Reinhard and Kutoyants Yury A.
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Kutoyants Yury A.: Université du Maine, Laboratoire de Statistique et Processus, Le Mans cedex 9, Frankreich

Statistics & Risk Modeling, 2009, vol. 27, issue 4, 309-326

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.

Keywords: diffusions; inhomogeneity in time; periodicity; continuous signals; local asymptotic normality (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1524/stnd.2009.1064

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