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Partial mean field limits in heterogeneous networks

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  • 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
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    1. 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.
    2. 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.
    3. 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.
    4. Takashi Ichinomiya, 2012. "Bouchaud-M\'ezard model on a random network," Papers 1209.2467, arXiv.org.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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