An extension of Skorohod’s almost sure representation theorem
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- by David Blackwell and Lester E. Dubins PDF
- Proc. Amer. Math. Soc. 89 (1983), 691-692 Request permission
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
- A. V. Skorohod, Limit theorems for stochastic processes, Teor. Veroyatnost. i Primenen. 1 (1956), 289–319 (Russian, with English summary). MR 0084897
Additional Information
- © Copyright 1983 American Mathematical Society
- 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