Premium
On cusp location estimation for perturbed dynamical systems
Author(s) -
Kutoyants Yury A.
Publication year - 2019
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12391
Subject(s) - mathematics , cusp (singularity) , estimator , consistency (knowledge bases) , singularity , position (finance) , location parameter , strong consistency , diffusion process , mathematical analysis , diffusion , statistics , geometry , physics , knowledge management , innovation diffusion , finance , computer science , economics , thermodynamics
We consider the problem of parameter estimation in the case of observation of the trajectory of the diffusion process. We suppose that the drift coefficient has a singularity of cusp type and that the unknown parameter corresponds to the position of the point of the cusp. The asymptotic properties of the maximum likelihood estimator and Bayesian estimators are described in the asymptotic of small noise , that is, as the diffusion coefficient tends to zero. The consistency, limit distributions, and the convergence of moments of these estimators are established.