Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An extension of Skorohod’s almost sure representation theorem


Authors: David Blackwell and Lester E. Dubins
Journal: Proc. Amer. Math. Soc. 89 (1983), 691-692
MSC: Primary 60B10
DOI: https://doi.org/10.1090/S0002-9939-1983-0718998-0
MathSciNet review: 718998
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Skorohod discovered that if a sequence ${Q_n}$ of countably additive probabilities on a Polish space converges in the weak star topology, then, on a standard probability space, there are ${Q_n}$-distributed ${f_n}$ which converge almost surely. This note strengthens Skorohod’s result by associating, with each probability $Q$ on a Polish space, a random variable ${f_Q}$ on a fixed standard probability space so that for each $Q$, (a) ${f_Q}$ has distribution $Q$ and (b) with probability 1, ${f_P}$ is continuous at $P = Q$.


References [Enhancements On Off] (What's this?)

  • A. V. Skorohod, Limit theorems for stochastic processes, Teor. Veroyatnost. i Primenen. 1 (1956), 289–319 (Russian, with English summary). MR 0084897

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60B10

Retrieve articles in all journals with MSC: 60B10


Additional Information

Keywords: Probability, almost sure convergence, weak convergence
Article copyright: © Copyright 1983 American Mathematical Society