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- W2051582227 abstract "We obtain new conditions for partial sums of an array with stationary rows to converge to a mixture of infinitely divisible distributions with finite variance. More precisely, we show that these conditions are necessary and sufficient to obtain conditional convergence . If the underlying σ -algebras are nested, conditional convergence implies stable convergence in the sense of Rényi. From this general result we derive new criteria expressed in terms of conditional expectations, which can be checked for many processes such as m -conditionally centered arrays or mixing arrays. When it is relevant, we establish the weak convergence of partial sum processes to a mixture of Lévy processes in the space of cadlag functions equipped with Skorohod's topology. The cases of Wiener processes, Poisson processes and Bernoulli distributed variables are studied in detail." @default.
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- W2051582227 date "2005-05-01" @default.
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- W2051582227 title "Conditional convergence to infinitely divisible distributions with finite variance" @default.
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- W2051582227 doi "https://doi.org/10.1016/j.spa.2004.12.006" @default.
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