Convergence of stochastic processes with random parameters. (English) Zbl 0601.60027
Let M and T be complete separable metric spaces, \(Y_ n: \Omega \times T\to M\) be a sequence of measurable stochastic processes and \(N_ n: \Omega \to T\) be a sequence of random parameters. The author studies the behavior of the sequence
\[
Y_ n(N_ n)=Y_ n(\omega,N_ n(\omega)): \Omega \to M
\]
in the sense of weak convergence. Under various mixing conditions on the sequence \((Y_ n)\) and some conditions on the behavior of the sequence \((N_ n)\), the author obtains the limit distribution of \(Y_ n(N_ n)\) provided a generalized Anscombe’s condition holds.
Reviewer: B.L.S.Prakasa Rao
MSC:
| 60F05 | Central limit and other weak theorems |
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