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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• Monte Carlo computation of multiple weak singular integrals of spherical and Volterra's type
• A simple Monte Carlo method for solving of Navier-Stokes Equations
• 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
• Unbiased Monte Carlo estimation for solving of linear integral equation, with error estimate