CLT for continuous random processes under approximations terms

2013/03/31 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1 · 1 citation
Computer Science · #Data Management and Algorithms #Rough Sets and Fuzzy Logic #Bayesian Methods and Mixture Models

paper · pdf · doi:10.48550/arxiv.1304.0250

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.

Citations

• Asymptotic exponential bounds for MLE deviation under minimal conditions via classical and generic chaining methods
• Exact exponential bounds for the random field maximum distribution via the majoring measures (generic chaining)

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