A New Mixing Condition
In this paper a new mixing condition for sequences of random variables is considered. This mixing condition is termed ÃƒÂ£-mixing. Whereas mixing conditions such as ÃƒÂ¡-mixing are typically defined in terms of entire ÃƒÂ³-fields of sets generated by random variables in the distant past and future, ÃƒÂ£-mixing is defined in terms of a smaller class of sets: the finite dimensional cylinder sets. This leads to a definition of mixing more general than those in current use. A Rosenthal inequality, law of large numbers, and functional central limit theorem are proved for ÃƒÂ£-mixing processes.
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- Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.