Abstract: In this paper, we shall be concerned with weak convergence of the randomly indexed versions of the standard and “independence” empirical processes, in the general framework of stochastic processes indexed by classes of functions and without any distributional assumption. We obtain, in the limit, some generalizations of well-known Gaussian fields such that those arising with a deterministic index are embedded as a special case.

1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: Kac empirical process, random sample size, generalized -Brownian fields, Donsker classes, independence empirical process.