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Occupation time limits of inhomogeneous Poisson systems of independent particles

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  • Bojdecki, T.
  • Gorostiza, L.G.
  • Talarczyk, A.

Abstract

We prove functional limits theorems for the occupation time process of a system of particles moving independently in according to a symmetric [alpha]-stable Lévy process, and starting from an inhomogeneous Poisson point measure with intensity measure , and other related measures. In contrast to the homogeneous case ([gamma]=0), the system is not in equilibrium and ultimately it becomes locally extinct in probability, and there are more different types of occupation time limit processes depending on arrangements of the parameters [gamma],d and [alpha]. The case [gamma]

Suggested Citation

  • Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2008. "Occupation time limits of inhomogeneous Poisson systems of independent particles," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 28-52, January.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:1:p:28-52
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    References listed on IDEAS

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    1. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems I: Long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 1-18, January.
    2. Deuschel, Jean-Dominique & Wang, Kongming, 1994. "Large deviations for the occupation time functional of a Poisson system of independent Brownian particles," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 183-209, August.
    3. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems II: Critical and large dimensions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 19-35, January.
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    Cited by:

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    2. Zhang, Xili & Xiao, Weilin, 2017. "Arbitrage with fractional Gaussian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 620-628.
    3. Milos, Piotr, 2009. "Occupation times of subcritical branching immigration systems with Markov motions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3211-3237, October.

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