IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v129y2019i12p4998-5036.html
   My bibliography  Save this article

Partial mean field limits in heterogeneous networks

Author

Listed:
  • Chong, Carsten
  • Klüppelberg, Claudia

Abstract

We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To capture these effects, we define a partial mean field system, and prove a law of large numbers with explicit bounds on the mean squared error. Furthermore, a large deviation result is established under reasonable assumptions. The theory will be illustrated by several examples: on the one hand, we recover the classical results of chaos propagation for homogeneous systems, and on the other hand, we demonstrate the validity of our assumptions for quite general heterogeneous networks including those arising from preferential attachment random graph models.

Suggested Citation

  • Chong, Carsten & Klüppelberg, Claudia, 2019. "Partial mean field limits in heterogeneous networks," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4998-5036.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:12:p:4998-5036
    DOI: 10.1016/j.spa.2018.12.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918307579
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2018.12.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Finnoff, William, 1993. "Law of large numbers for a general system of stochastic differential equations with global interaction," Stochastic Processes and their Applications, Elsevier, vol. 46(1), pages 153-182, May.
    2. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers & Justin A. Sirignano, 2015. "Large Portfolio Asymptotics For Loss From Default," Mathematical Finance, Wiley Blackwell, vol. 25(1), pages 77-114, January.
    3. Battiston, Stefano & Delli Gatti, Domenico & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2012. "Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1121-1141.
    4. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
    5. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers & Justin A. Sirignano, 2011. "Large Portfolio Asymptotics for Loss From Default," Papers 1109.1272, arXiv.org, revised Feb 2015.
    6. Budhiraja, Amarjit & Wu, Ruoyu, 2016. "Some fluctuation results for weakly interacting multi-type particle systems," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2253-2296.
    7. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
    8. Takashi Ichinomiya, 2012. "Bouchaud-M\'ezard model on a random network," Papers 1209.2467, arXiv.org.
    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. Seroussi, Inbar & Sochen, Nir, 2020. "Localization phase transition in stochastic dynamics on networks with hub topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    2. Sergey Nadtochiy & Mykhaylo Shkolnikov, 2017. "Particle systems with singular interaction through hitting times: application in systemic risk modeling," Papers 1705.00691, arXiv.org.
    3. Stojkoski, Viktor & Karbevski, Marko & Utkovski, Zoran & Basnarkov, Lasko & Kocarev, Ljupco, 2021. "Evolution of cooperation in networked heterogeneous fluctuating environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    4. Venkatasubramanian, Venkat & Luo, Yu & Sethuraman, Jay, 2015. "How much inequality in income is fair? A microeconomic game theoretic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 120-138.
    5. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    6. Agostino Capponi & Xu Sun & David D. Yao, 2020. "A Dynamic Network Model of Interbank Lending—Systemic Risk and Liquidity Provisioning," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1127-1152, August.
    7. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, January.
    8. Smerlak, Matteo, 2016. "Thermodynamics of inequalities: From precariousness to economic stratification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 40-50.
    9. Marco Raberto & Silvano Cincotti & Sergio Focardi & Michele Marchesi, 2003. "Traders' Long-Run Wealth in an Artificial Financial Market," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 255-272, October.
    10. Jean-David Fermanian, 2020. "On the Dependence between Default Risk and Recovery Rates in Structural Models," Annals of Economics and Statistics, GENES, issue 140, pages 45-82.
    11. Jiong Liu & R. A. Serota, 2023. "Rethinking Generalized Beta family of distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-14, February.
    12. Geoff Willis & Juergen Mimkes, 2004. "Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution," Microeconomics 0408001, University Library of Munich, Germany.
    13. Caballero, Diego & Lucas, André & Schwaab, Bernd & Zhang, Xin, 2020. "Risk endogeneity at the lender/investor-of-last-resort," Journal of Monetary Economics, Elsevier, vol. 116(C), pages 283-297.
    14. G. Willis, 2004. "Laser Welfare: First Steps in Econodynamic Engineering," Papers cond-mat/0408227, arXiv.org.
    15. Alessandro Pluchino & Alessio Emanuele Biondo & Andrea Rapisarda, 2018. "Talent Versus Luck: The Role Of Randomness In Success And Failure," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(03n04), pages 1-31, May.
    16. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2023. "Microfounding GARCH models and beyond: a Kyle-inspired model with adaptive agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(3), pages 599-625, July.
    17. Zhiyuan Liu & R. A. Serota, 2017. "On absence of steady state in the Bouchaud-M\'ezard network model," Papers 1704.02377, arXiv.org.
    18. Ma, Tao & Holden, John G. & Serota, R.A., 2013. "Distribution of wealth in a network model of the economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2434-2441.
    19. Konstantinos Spiliopoulos & Jia Yang, 2018. "Network effects in default clustering for large systems," Papers 1812.07645, arXiv.org, revised Feb 2020.
    20. Zoltan Kuscsik & Denis Horvath, 2007. "Statistical properties of agent-based market area model," Papers 0710.0459, arXiv.org.

    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:129:y:2019:i:12:p:4998-5036. 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.