IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v56y1995i2p295-305.html
   My bibliography  Save this article

Convergence of independent particle systems

Author

Listed:
  • Hoffman, John R.
  • Rosenthal, Jeffrey S.

Abstract

We consider a system of particles moving independently on a countable state space, according to a general (non-space-homogeneous) Markov process. Under mild conditions, the number of particles at each site will converge to a product of independent Poisson distributions; this corresponds to settling to an ideal gas. We derive bounds on the rate of this convergence. In particular, we prove that the variation distance to stationarity decreases proportionally to the sum of squares of the probabilities of each particle to be at a given site. We then apply these bounds to some examples. Our methods include a simple use of the Chen-Stein lemma about Poisson convergence. Our results require certain strong hypotheses, which further work might be able to eliminate.

Suggested Citation

  • Hoffman, John R. & Rosenthal, Jeffrey S., 1995. "Convergence of independent particle systems," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 295-305, April.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:2:p:295-305
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(94)00075-5
    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. Liggett, T. M. & Port, S. C., 1988. "Systems of independent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 28(1), pages 1-22, April.
    2. Unknown, 1993. "Book Reviews," Journal of Agricultural Cooperation, National Council of Farmer Cooperatives, vol. 8, pages 1-8.
    3. S. George, 1993. "Book Review," Foreign Trade Review, , vol. 27(4), pages 439-440, January.
    4. Unknown, 1993. "Book Reviews," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 37(3), pages 1-10, December.
    5. Unknown, 1993. "Book Reviews," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 37(2), pages 1-22, August.
    6. Unknown, 1993. "Book Reviews," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 61(03), pages 1-5, December.
    Full references (including those not matched with items on IDEAS)

    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. Gerald T. Garvey, 1994. "Why Labour Is Not Different," Agenda - A Journal of Policy Analysis and Reform, Australian National University, College of Business and Economics, School of Economics, vol. 1(1), pages 5-12.
    2. Jean-Philippe Aguilar & Cyril Coste & Hagen Kleinert & Jan Korbel, 2016. "Distributional Mellin calculus in $\mathbb{C}^n$, with applications to option pricing," Papers 1611.03239, arXiv.org, revised Nov 2016.
    3. Tao Ma & R. A. Serota, 2013. "A Model for Stock Returns and Volatility," Papers 1305.4173, arXiv.org.
    4. MacDougall, Gordon P., 2011. "Book Review," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 50(1).
    5. Newell, G. F., 1998. "The rolling horizon scheme of traffic signal control," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(1), pages 39-44, January.
    6. Lamberton, Donald M., 1998. "Information economics research: Points of departure," Information Economics and Policy, Elsevier, vol. 10(3), pages 325-330, September.
    7. Marc Lavoie, 2003. "Kaleckian Effective Demand and Sraffian Normal Prices: Towards a reconciliation," Review of Political Economy, Taylor & Francis Journals, vol. 15(1), pages 53-74.

    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:56:y:1995:i:2:p:295-305. 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.