2009/03/29 by Reinhard Hoepfner, Hoepfner, Reinhard, Yury A. Kutoyants +2 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #60 J 60 #62 F 12 #Diffusion and Search Dynamics #FOS: Mathematics #Mathematical Biology Tumor Growth #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics #math.ST #msc:12 #msc:60 #msc:62 #stat.TH
paper · pdf · doi:10.48550/arxiv.0903.5061
42 pages
openalex publication_date 2009/03/29 · arxiv created 2010/03/17 · arxiv updated 2010/03/18 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28
We consider a diffusion (ξt)t≥ 0 with some T-periodic time dependent input term contained in the drift: under an unknown parameter \vth∈Θ, some discontinuity - an additional periodic signal - occurs at times kT+\vth, k∈\bbn. Assuming positive Harris recurrence of (ξkT)k∈\bbn0 and exploiting the periodicity structure, we prove limit theorems for certain martingales and functionals of the process (ξt)t≥ 0. They allow to consider the statistical model parametrized by \vth∈Θ locally in small neighbourhoods of some fixed \vth, with radius 1/n as \nto. We prove convergence of local models to a limit experiment studied by Ibragimov and Khasminskii [IH 81] and discuss the behaviour of estimators under contiguous alternatives.