Discretization error for the maximum of a Gaussian field

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Azais, Jean-Marc¹  Chassan, Malika¹ 

[1] Univ Paul Sabatier, Inst Math Toulouse, UMR 5219, 118 Route Narbonne, F-31062 Toulouse 9, France

关键词: Gaussian field;    Field maximum;    Discretization error;    Slepian model;   

DOI  :  10.1016/j.spa.2019.02.002

来源: Elsevier

【 摘 要 】

The paper considers the difference between (a) the true maximum of a Gaussian field on a square and (b) its maximum on a regular grid. This difference is called the discretization error. A kind of Slepian model is used to study the behavior of the field around the location of the maximum. We show that the normalized discretization error can be bounded by a quantity that converges to a uniform variable, depending on the Hessian matrix at the point of the maximum. The bound is applied to simulated and real data (satellite positioning data). (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free