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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
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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 

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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