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Some remarks on the uniform weak convergence of stochastic processes

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  • Arcones, Miguel A.

Abstract

It is known that the uniform weak convergence of a sequence of stochastic processes is equivalent to the finite dimensional convergence, plus an asymptotic equicontinuity condition with respect to any pseudometric which makes the parameter space totally bounded. Here, we see that in this characterization, it is possible to take an intrinsic metric of the process. This is applied to obtain necessary and sufficient conditions for the weak convergence of local U-processes.

Suggested Citation

  • Arcones, Miguel A., 1996. "Some remarks on the uniform weak convergence of stochastic processes," Statistics & Probability Letters, Elsevier, vol. 28(1), pages 41-49, June.
    • Handle: RePEc:eee:stapro:v:28:y:1996:i:1:p:41-49
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    Cited by:

    1. Miguel Arcones & Hengjian Cui & Yijun Zuo, 2006. "Empirical depth processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 151-177, June.
    2. Arcones, Miguel A., 1995. "Asymptotic normality of multivariate trimmed means," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 43-53, October.

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