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Teor. Veroyatnost. i Primenen., 1998, Volume 43, Issue 3, Pages 561–576 (Mi tvp1560)  

On the weak convergence of vector-valued continuous random processes

Zhong Gen Suab

a Research Institute of Mathematics, Fudan University, China
b Department of Mathematics, Hangzhou University, China

Abstract: In this paper we shall establish some results on weak convergence for vector-valued continuous random processes, among which are vector-valued sub-Gaussian processes, vector-valued random processes satisfying Lipschitz conditions, and random Fourier series with vector-valued coefficients. The results obtained can be considered as corresponding extensions of those in the real setting. Our basic ideas stem from Fernique's recent works.

Keywords: weak convergence, vector-valued Gaussian process, metric entropy, type 2 space.

DOI: https://doi.org/10.4213/tvp1560

Full text: PDF file (768 kB)

English version:
Theory of Probability and its Applications, 1999, 43:3, 463–476

Bibliographic databases:

Received: 13.03.1996

Citation: Zhong Gen Su, “On the weak convergence of vector-valued continuous random processes”, Teor. Veroyatnost. i Primenen., 43:3 (1998), 561–576; Theory Probab. Appl., 43:3 (1999), 463–476

Citation in format AMSBIB
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\pages 561--576
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\jour Theory Probab. Appl.
\yr 1999
\vol 43
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\pages 463--476
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