Nonasymptotic Formulae for the Distribution of the Maximum of Smooth Gaussian Processes

Abstract

We derive an integral formula for the density of the maximum of smooth Gaussian processes. This expression induces explicit lower and upper bounds which are in general asymptotic to the density. Our constructive approach relies on a geometric representation of Gaussian processes involving a unit speed parameterized curve embedded in the unit sphere.

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Document Details

Document Type
Technical Report
Publication Date
Aug 11, 1994
Accession Number
ADA284741

Entities

People

  • C. Posse
  • J. Diebolt

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Covariance
  • Curvature
  • Data Science
  • Differential Geometry
  • Gaussian Processes
  • Geometry
  • Information Science
  • Integrals
  • Military Research
  • New York
  • Probability
  • Security
  • Sequences
  • Statistics
  • Stochastic Processes
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.