Matrix normalized convergence of a Lévy process to normality at zero

Ross A. Maller and David M. Mason

Stochastic Processes and their Applications, 2015, vol. 125, issue 6, 2353-2382

Abstract: We give a necessary and sufficient condition for a d-dimensional Lévy process to be in the matrix normalized domain of attraction of a d-dimensional normal random vector, as t↓0. This transfers to the Lévy case classical results of Feller, Khinchin, Lévy and Hahn and Klass for random walks. A specific construction of the norming matrix is given, and it is shown that centering constants may be taken as 0. Functional and self-normalization results are also given, as is a necessary and sufficient condition for the process to be in the matrix normalized domain of partial attraction of the normal.

Keywords: Lévy process; Matrix normalization; Domain of attraction; Domain of partial attraction; Normal distribution; Self-normalized process; Quadratic variation process (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:6:p:2353-2382

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DOI: 10.1016/j.spa.2015.01.003

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