Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems

Luis G. Gorostiza (), Reyla A. Navarro () and Eliane R. Rodrigues ()
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Luis G. Gorostiza: Departamento de Mathematicas, Centro de Investigacion y de Estudios Avanzados, LRSP
Reyla A. Navarro: Departamento de Fisica y Mathematicas, Universidad de Las Americas
Eliane R. Rodrigues: Instituto de Mathematicas, UNAM

No lrsp-TRS401, RePAd Working Paper Series from Département des sciences administratives, UQO

Abstract: Several long-range dependence, self-similar Gaussian processes arise from asymptotics of some classes of spatially distributed particle systems and superprocesses. The simplest examples are fractional Brownian motion and sub-fractional fractional Brownian motion, the latter being intermediate between Brownian motion and fractional Brownian motion. In this paper we focus mainly on long-range dependence processes that arise from occupation time fluctuations of immigration particle systems with or without branching, and we study their properties. Some long-range dependence non-Gaussian processes that appear in a similar way are also mentioned.

Keywords: long-range dependence; long memory; self-similar Gaussian process; fractional Brownian motion; sub-fractional Brownian motion; branching particle system; immigration; superprocess; occupation time; fluctuation (search for similar items in EconPapers)
JEL-codes: C10 C40 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2004-01-08
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