Zero-One Laws for Gaussian Measures on Banach Space,

Abstract

Let Beta be a real separable Banach space, mu a Gaussian measure on the Borel sigma-field of Beta, and B sub mu (Beta) the completion of the Borel sigma-field under mu. If G belongs to B sub mu (Beta) is a subgroup, it is shown that mu(G) = 0 or 1, extending a result due to Kallianpur and Jain. Necessary and sufficient conditions are given for mu(G) = 1 for the case where G is the range of a bounded linear operator. These results are then applied to obtain a number of 0-1 statements for the sample functions properties of a Gaussian stochastic process. The zero-one law is then extended to a class of non-Gaussian measures, and applications are given to some non-Gaussian stochastic processes. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1971
Accession Number
AD0734657

Entities

People

  • Charles R. Baker

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Banach Space
  • Functional Analysis
  • Mathematics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.

Technology Areas

  • Space