Weak Convergence of High Level Exceedances by a Stationary Sequence,

Abstract

In the paper the author considers a stationary sequence ((xi sub n):n = 1, 2 ... ) satisfying weak dependence restrictions. For each n the point process (N sub n) is defined to consist of the exceedances of a certain level (u sub n) (i.e. the instants j for which (xi sub j) > (u sub n). It is shown that the point processes (N sub n) converge weakly (as random elements of the natural metric space to which they belong) to a Poisson process.

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1974
Accession Number
AD0781728

Entities

People

  • M. Ross Leadbetter

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Convergence
  • Sequences
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.

Technology Areas

  • Space