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- W1980535956 abstract "In this paper, we give necessary and sufficient conditions for a stationary sequence of random variables with values in a separable Hilbert space to satisfy the conditional central limit theorem introduced in Dedecker and Merlevède (Ann. Probab. 30 (2002) 1044–1081). As a consequence, this theorem implies stable convergence of the normalized partial sums to a mixture of normal distributions. We also establish the functional version of this theorem. Next, we show that these conditions are satisfied for a large class of weakly dependent sequences, including strongly mixing sequences as well as mixingales. Finally, we present an application to linear processes generated by some stationary sequences of H-valued random variables." @default.
- W1980535956 created "2016-06-24" @default.
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- W1980535956 date "2003-12-01" @default.
- W1980535956 modified "2023-09-30" @default.
- W1980535956 title "The conditional central limit theorem in Hilbert spaces" @default.
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- W1980535956 doi "https://doi.org/10.1016/j.spa.2003.07.004" @default.
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