IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v118y2008i1p28-52.html
   My bibliography  Save this article

Occupation time limits of inhomogeneous Poisson systems of independent particles

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(07)00050-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuqiang Li & Yimin Xiao, 2012. "Occupation Time Fluctuations of Weakly Degenerate Branching Systems," Journal of Theoretical Probability, Springer, vol. 25(4), pages 1119-1152, December.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bojdecki, Tomasz & Talarczyk, Anna, 2012. "Particle picture interpretation of some Gaussian processes related to fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2134-2154.
    2. Araneda, Axel A. & Bertschinger, Nils, 2021. "The sub-fractional CEV model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    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.
    4. Li, Yuqiang, 2011. "Fluctuation limits of site-dependent branching systems in critical and large dimensions," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1604-1611, November.
    5. Yuqiang Li & Yimin Xiao, 2012. "Occupation Time Fluctuations of Weakly Degenerate Branching Systems," Journal of Theoretical Probability, Springer, vol. 25(4), pages 1119-1152, December.
    6. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2015. "From intersection local time to the Rosenblatt process," Journal of Theoretical Probability, Springer, vol. 28(3), pages 1227-1249, September.
    7. Talarczyk, Anna, 2008. "A functional ergodic theorem for the occupation time process of a branching system," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 847-853, May.
    8. Yan, Litan & Shen, Guangjun, 2010. "On the collision local time of sub-fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 296-308, March.
    9. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    10. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2005. "A Long Range Dependence Stable Process and an Infinite Variance Branching System," RePAd Working Paper Series lrsp-TRS425, Département des sciences administratives, UQO.
    11. Tudor, Constantin, 2008. "Inner product spaces of integrands associated to subfractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2201-2209, October.
    12. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2004. "Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Cases of Large and Critical Dimensions," RePAd Working Paper Series lrsp-TRS404, Département des sciences administratives, UQO.
    13. D. A. Dawson & L. G. Gorostiza & A. Wakolbinger, 2001. "Occupation Time Fluctuations in Branching Systems," Journal of Theoretical Probability, Springer, vol. 14(3), pages 729-796, July.
    14. Luis G. Gorostiza & Reyla A. Navarro & Eliane R. Rodrigues, 2004. "Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems," RePAd Working Paper Series lrsp-TRS401, Département des sciences administratives, UQO.
    15. 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.
    16. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
    17. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2004. "Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Case of Long-Range Dependence," RePAd Working Paper Series lrsp-TRS402, Département des sciences administratives, UQO.
    18. 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.
    19. Shen, Guangjun & Chen, Chao, 2012. "Stochastic integration with respect to the sub-fractional Brownian motion with H∈(0,12)," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 240-251.
    20. Sun, Hongyan, 2013. "A large deviation theorem for a branching Brownian motion with random immigration," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1559-1566.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:118:y:2008:i:1:p:28-52. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.