CLT for continuous random processes under approximations terms

Abstract

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.

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Cited by in corpus (3)

• Each Random Variable in separable Banach Space belongs to the Domain of Definition of some inverse to compact linear non-random operator
• Exact exponential tail estimations in the Law of Iterated Logarithm for Bochner's mixed Lebesgue spaces
• Random processes and Central Limit Theorem in Besov spaces