Central Limit Theorem in Lebesgue-Riesz spaces for weakly dependent random sequences
M.R.Formica, E.Ostrovsky, L.Sirota
TL;DR
This paper establishes conditions under which the Central Limit Theorem holds in Lebesgue-Riesz spaces for weakly dependent random sequences, expanding understanding of CLT in functional spaces.
Contribution
It provides new sufficient conditions for the CLT in Lebesgue-Riesz spaces for strongly mixing sequences, addressing both asymptotic and non-asymptotic cases.
Findings
Sufficient conditions for CLT in L(p) spaces established
Results apply to strongly mixing (Rosenblatt) sequences
Both asymptotic and non-asymptotic approaches analyzed
Abstract
We deduce sufficient conditions for the Central Limit Theorem (CLT) in the Lebesgue-Riesz space L(p) defined on some measure space for the sequence of centered random variables satisfying the strong mixing (Rosenblatt) condition. We investigate the asymptotical as well as non-asymptotical approach.
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Taxonomy
TopicsProbability and Risk Models · Stochastic processes and financial applications · Financial Risk and Volatility Modeling