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.
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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
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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
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