A Long Range Dependence Stable Process and an Infinite Variance Branching System

T. Bojdecki (), Luis G. Gorostiza () and A. Talarczyk ()
Additional contact information
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

No lrsp-TRS425, RePAd Working Paper Series from Département des sciences administratives, UQO

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 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.

Keywords: Branching particle system; occupation time fluctuation; functional limit theorem; stable process; long range dependence. (search for similar items in EconPapers)
JEL-codes: C10 C40 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2005-11-14
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.repad.org/ca/on/lrsp/TRS425.pdf First version, 2005 (application/pdf)
Our link check indicates that this URL is bad, the error code is: 500 Can't connect to www.repad.org:80 (No such host is known. )

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pqs:wpaper:102006

Access Statistics for this paper

More papers in RePAd Working Paper Series from Département des sciences administratives, UQO Contact information at EDIRC.
Bibliographic data for series maintained by Christian Calmes ().