Hostname: page-component-5b777bbd6c-7sgmh Total loading time: 0 Render date: 2025-06-21T20:17:12.684Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak convergence of probability measures and random functions in the function space D[0,∞)

Published online by Cambridge University Press:  14 July 2016

Torgny Lindvall
Torgny Lindvall*
Affiliation:
University of Göteborg
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper extends the theory of weak convergence of probability measures and random functions in the function space D[0,1] to the case D [0,∞), elaborating ideas of C. Stone and W. Whitt. 7)[0,∞) is a suitable space for the analysis of many processes appearing in applied probability.

Keywords

WEAK CONVERGENCERANDOM FUNCTIONS AND PROBABILITY MEASURESEXTENSION OF SKOROHOD'S TOPOLOGY TO THE SEMI-INFINITE INTERVAL CASECOMPLETE SEPARABLE METRIC SPACE
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 109 - 121
Copyright
Copyright © Applied Probability Trust 1973 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Billingsley, P. (1968) Convergence of Probability Measures. John Wiley, New York.Google Scholar
[2] Kolmogorov, N. A. (1956) On Skorohod convergence. Theor. Probability Appl. 1, 215–222.CrossRefGoogle Scholar
[3] Prohorov, Yu. (1956) Convergence of random processes and limit theorems in probability theory. Theor. Probability Appl. 1, 157–214.CrossRefGoogle Scholar
[4] Skorohod, A. (1956) Limit theorems for stochastic processes. Theor. Probability Appl. 1, 262–290.Google Scholar
[5] Stone, C. (1963) Weak convergence of stochastic processes defined on a semifinite time interval. Proc. Amer. Math. Soc. 14, 694–696.CrossRefGoogle Scholar
[6] Whitt, W. (1970) Weak convergence of probability measures on the function space C[0, 8). Ann. Math. Statist. 41, 939–944.CrossRefGoogle Scholar
[7] Whitt, W. (1971) Weak convergence of probability measures on the function space D[0, 8). Technical report, Yale University.Google Scholar
[8] Whitt, W. (1971) Representation and convergence of point processes on the line. Technical report, Yale University.Google Scholar
[9] Whitt, W. (1972) Stochastic Abelian and Tauberian theorems. Zeit. Wahrscheinlichkeitsth. 22, 251–267.CrossRefGoogle Scholar