TY - JOUR
T1 - Matrix normalized convergence of a Lévy process to normality at zero
AU - Maller, Ross A.
AU - Mason, David M.
N1 - Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - 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.
AB - 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.
KW - Domain of attraction
KW - Domain of partial attraction
KW - Lévy process
KW - Matrix normalization
KW - Normal distribution
KW - Quadratic variation process
KW - Self-normalized process
UR - http://www.scopus.com/inward/record.url?scp=84939974747&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2015.01.003
DO - 10.1016/j.spa.2015.01.003
M3 - Article
SN - 0304-4149
VL - 125
SP - 2353
EP - 2382
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 6
ER -