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

2010/03/18 by Reinhard Hoepfner, Hoepfner, Reinhard, Yury A. Kutoyants +2
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60 J 60 #62 F 12 #Diffusion and Search Dynamics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Quantum chaos and dynamical systems #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.ST #msc:12 #msc:60 #msc:62 #stat.TH

paper · pdf · doi:10.48550/arxiv.1003.3546

arxiv created 2010/03/18 · openalex publication_date 2010/03/18 · arxiv updated 2010/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a diffusion (ξ_t)_{t≥ 0} whose drift involves a T-periodic signal. T is fixed and known, whereas the signal depends on an unknown d-dimensional parameter ϑ∈Θ. Assuming positive Harris recurrence of the grid chain (ξ_kT)_k∈ℕ0 and exploiting the periodic structure of 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.

Citations

• Estimating discontinuous periodic signals in a non-time homogeneous diffusion process
• Statistics of Random Processes

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