CRITERIA FOR THE CONTINUITY AND DIFFERENTIABILITY OF VECTOR PARAMETER PROCESSES,

Abstract

Let f(x) be a real or vector valued random process whose parameter set R is a bounded set in Euclidean n-space. Following the usual terminology, a version of f(x) is any process f tilde (x) defined on R which satisfies P(f(x) = f tilde (x)) =1 for each x epsilon R. It is sometimes useful to assert that there exists a version of f(x) which is (with probability one) continuous, Holder continuous, or perhaps differentiable in some component. Also estimates of the type P(sup (x epsilon R)/f(x)/> epsilon) may be desired for these versions. Illustrative examples are given.

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1967
Accession Number
AD0690117

Entities

People

  • Harold J. Kushner

Organizations

  • Brown University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Aeronautics
  • Continuity
  • Probability

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space