T. Bojdecki () (Institute of Mathematics, University of Warsaw) Luis G. Gorostiza () (Departamento de Mathematicas, Centro de Investigacion y de Estudios Avanzados, LRSP) A. Talarczyk () (Institute of Mathematics, University of Warsaw)
Abstract
We prove a functional limit theorem for the rescaled occupation time fluctuations of a (d, , )- branching particle system (particles moving in Rd according to a symmetric -stable L´evy process, branching law in the domain of attraction of a (1 + )-stable law, 0 < < 1, uniform Poisson initial state) in the case of intermediate dimensions, / < d < (1 + )/ . The limit is a process of the form K, where K is a constant, is the Lebesgue measure on Rd, and = (t)t0 is a (1+ )-stable process which has long range dependence. There are two long range dependence regimes, one for all > d/(d + ), which coincides with the case of finite variance branching ( = 1), and another one for d/(d + ), where the long range dependence depends on the value of . The long range dependence is characterized by a dependence exponent which describes the asymptotic behavior of the codi erence of increments of on intervals far apart, and which is d/ for the first case and (1 + - d/(d + ))d/ for the second one. The convergence proofs use techniques of S0(Rd)-valued processes.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number
lrsp-TRS425.
Length: 21 pages Date of creation: 14 Nov 2005 Date of revision: Handle: RePEc:pqs:wpaper:102006
Contact details of provider: Postal: Pavillon Lucien Brault, 101 rue Saint Jean-Bosco, Gatineau (Qu�bec) J8Y 3G5 Phone: (819) 595-3900 Fax: (819) 773-1747 Web page: http://www.repad.org/ More information through EDIRC
For technical questions regarding this item, or to correct its listing, contact: (Christian Calmes).
Find related papers by JEL classification: C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
This paper has been announced in the following NEP Reports: