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The Central Limit Theorem for Empirical Processes Under Local Conditions: The Case of Radon Infinitely Divisible Limits without Gaussian Component
Weak convergence results are obtained for empirical processes indexed by classes &" of functions in the case of infinitely divisible purely Poisson (in particular, stable) Radon limits, under conditions on the local modulus of the processes {f(X): f 6 &"} ("bracketing" conditions).They extend (and slightly improve upon) a central limit …