Conditional convergence to infinitely divisible distributions with finite variance

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:115

Article

Dedecker, J ; Louhichi, S

关键词: infinitely divisible distributions;    Levy processes;    stable convergence;    triangular arrays;    mixing processes;   

DOI  :  10.1016/j.spa.2004.12.006

来源: Elsevier

【 摘 要 】

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 sigma-algebras are nested, conditional convergence implies stable convergence in the sense of Renyi. 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 Levy 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. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free