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Weak convergence of sequences of random elements with random indices

Published online by Cambridge University Press:  24 October 2008

M. Csörgő  and
Z. Rychlik
M. Csörgő
Affiliation:
Carleton University and MariaCurie-Sklodowska University, Lublin
Z. Rychlik
Affiliation:
Carleton University and MariaCurie-Sklodowska University, Lublin
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Extract

Let (S, d) be a separable metric space equipped with its Borel σ field . Let {Yn, n ≥ 1} be a sequence of S-valued random elements defined on a probability space (Ω, , p). Assume Yn ⇒ Y converges weakly to an S-valued random element Y. Let {Nn, n ≥ 1} be a sequence of positive integer-valued random variables defined on the same probability space (Ω, , p).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 1 , July 1980 , pp. 171 - 174
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

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