LAMN in a class of parametric models for null recurrent diffusion

2017/11/06 by Reinhard Höpfner, Höpfner, Reinhard, Carina Zeller +1
Mathematics · #60 J 6 #62 F 12 #62 M 05 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1711.01776

openalex publication_date 2017/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study statistical models for one-dimensional diffusions which are recurrent null. A first parameter in the drift is the principal one, and determines regular varying rates of convergence for the score and the information process. A finite number of other parameters, of secondary importance, introduces additional flexibility for the modelization of the drift, and does not perturb the null recurrent behaviour. Under time-continuous observation we obtain local asymptotic mixed normality (LAMN), state a local asymptotic minimax bound, and specify asymptotically optimal estimators.

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