A characterization of $\boldsymbol{m}$-dependent stationary infinitely divisible sequences with applications to weak convergence
Harrelson, D. ; Houdré, C.
Ann. Probab., Tome 31 (2003) no. 1, p. 849-881 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
$m$-dependent stationary infinitely divisible sequences are characterized as a class of generalized finite moving average sequences via the structure of the associated Lévy measure. This characterization is used to find necessary and sufficient conditions for the weak convergence of centered and normalized partial sums of $m$-dependent stationary infinitely divisible sequences. Partial sum convergence for stationary infinitely divisible sequences that can be approximated by $m$-dependent ones is then studied.
Publié le : 2003-04-14
Classification:  Infinitely divisible,  $m$-dependence,  stationary,  stable limit theorem,  60F05,  60E07,  60G10 
@article{1048516538,
     author = {Harrelson, D. and Houdr\'e, C.},
     title = {A characterization of $\boldsymbol{m}$-dependent stationary infinitely
divisible sequences with applications to weak convergence},
     journal = {Ann. Probab.},
     volume = {31},
     number = {1},
     year = {2003},
     pages = { 849-881},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1048516538}
}

Harrelson, D.; Houdré, C. A characterization of $\boldsymbol{m}$-dependent stationary infinitely
divisible sequences with applications to weak convergence. Ann. Probab., Tome 31 (2003) no. 1, pp.  849-881. http://gdmltest.u-ga.fr/item/1048516538/