Exact adaptive pointwise drift estimation for multidimensional ergodic diffusions
成果类型：
Article
署名作者：
Strauch, Claudia
署名单位：
University of Hamburg
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-014-0614-4
发表日期：
2016
页码：
361-400
关键词：
摘要：
The problem of pointwise adaptive estimation of the drift coefficient of a multivariate diffusion process is investigated. We propose an estimator which is sharp adaptive on scales of Sobolev smoothness classes. The analysis of the exact risk asymptotics allows to identify the impact of the dimension and other influencing values-such as the geometry of the diffusion coefficient-of the prototypical drift estimation problem for a large class of multidimensional diffusion processes. We further sketch generalizations of our results to arbitrary diffusions satisfying suitable Bernstein-type inequalities.