Weak convergence of sequences of random elements with random indices
- 1 July 1980
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 88 (1) , 171-174
- https://doi.org/10.1017/s0305004100057467
Abstract
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).Keywords
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