Probability Bounds for M-Skorohod Oscillations.

Abstract

Billingsley developed a widely used method for proving weak convergence with respect to the sup-norm and J -Skorohod topologies, once convergence of the finite-dimensional distributions has been established. Billingsley's method works not only for J oscillations, but also for M oscillations. This is done by identifying a common property of the J and M functions, called sub-triadditivity, and then showing that Billingsley's approach in the case of the J function can be adequately modified to apply to any sub-triadditive function. Keywords: Weak convergence; Skorohod topologies; Sub-triadditivity.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1986
Accession Number
ADA187981

Entities

People

  • Florin Avram
  • Murrad S. Taqqu

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Convergence
  • Inequalities
  • Intervals
  • Mathematics
  • New York
  • North Carolina
  • Oscillation
  • Probability
  • Random Variables
  • Scientific Research
  • Statistics
  • Stochastic Processes
  • Topology
  • Universities
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science/Meteorology
  • Mathematical Modeling and Probability Theory.