On the weak convergence of vector-valued continuous random processes

Zhong Gen Su<sup>ab

a</sup> 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.

Received: 13.03.1996

DOI: 10.4213/tvp1560

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

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