We formulate and prove a new sufficient conditions for Central Limit Theorem(CLT) in the space of continuous functions in the terms typical for the approximation theory. We prove that the conditions for continuous CLT obtained by N.C.Jain and M.B.Marcus are under some natural additional conditions necessary. We provide also some examples in order to show the exactness of obtained results and illustrate briefly the applications in the Monte-Carlo method.
A central limit theorem for a localized version of the SK model
Noise-stability and central limit theorems for effective resistance of random electric networks
Exactness of martingale approximation and the central limit theorem
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