IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v141y2021icp197-244.html
   My bibliography  Save this article

Mean field interaction on random graphs with dynamically changing multi-color edges

Author

Listed:
  • Bayraktar, Erhan
  • Wu, Ruoyu

Abstract

We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution of all the other nodes and the edges connected to it, while the edge dynamics depends only on the corresponding nodes it connects. Asymptotic results, including law of large numbers, propagation of chaos, and central limit theorems, are established. In contrast to the classic McKean–Vlasov limit, the limiting system exhibits a path-dependent feature in that the evolution of a given particle depends on its own conditional distribution given its past trajectory. We also analyze the asymptotic behavior of the system when the edge dynamics is accelerated. A law of large number and a propagation of chaos result is established, and the limiting system is given as independent McKean–Vlasov processes. Error between the two limiting systems, with and without acceleration in edge dynamics, is also analyzed.

Suggested Citation

  • Bayraktar, Erhan & Wu, Ruoyu, 2021. "Mean field interaction on random graphs with dynamically changing multi-color edges," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 197-244.
    • Handle: RePEc:eee:spapps:v:141:y:2021:i:c:p:197-244
    DOI: 10.1016/j.spa.2021.07.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414921001113
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2021.07.005?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. Kurtz, Thomas G. & Xiong, Jie, 1999. "Particle representations for a class of nonlinear SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 103-126, September.
    2. Graham, Carl, 1992. "McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 69-82, February.
    3. Bhamidi, Shankar & Budhiraja, Amarjit & Wu, Ruoyu, 2019. "Weakly interacting particle systems on inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2174-2206.
    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. Bayraktar, Erhan & Wu, Ruoyu, 2022. "Stationarity and uniform in time convergence for the graphon particle system," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 532-568.
    2. Bayraktar, Erhan & Wu, Ruoyu, 2023. "Graphon particle system: Uniform-in-time concentration bounds," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 196-225.

    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. Luçon, Eric, 2020. "Quenched asymptotics for interacting diffusions on inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6783-6842.
    2. Christa Cuchiero & Martin Larsson & Sara Svaluto-Ferro, 2018. "Probability measure-valued polynomial diffusions," Papers 1807.03229, arXiv.org.
    3. Lijun Bo & Tongqing Li & Xiang Yu, 2021. "Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence," Papers 2106.09978, arXiv.org, revised May 2022.
    4. E. Löcherbach, 2020. "Convergence to Equilibrium for Time-Inhomogeneous Jump Diffusions with State-Dependent Jump Intensity," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2280-2314, December.
    5. Detering, Nils & Fouque, Jean-Pierre & Ichiba, Tomoyuki, 2020. "Directed chain stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2519-2551.
    6. Gao, Yunshi, 2024. "Large deviations for mean field model in Erdős–Rényi graph," Statistics & Probability Letters, Elsevier, vol. 205(C).
    7. Lücke, Marvin & Heitzig, Jobst & Koltai, Péter & Molkenthin, Nora & Winkelmann, Stefanie, 2023. "Large population limits of Markov processes on random networks," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    8. Graham, Carl, 2011. "Convergence of multi-class systems of fixed possibly infinite sizes," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 31-35, January.
    9. Clini, Andrea, 2023. "Porous media equations with nonlinear gradient noise and Dirichlet boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 428-498.
    10. Bo, Lijun & Li, Tongqing & Yu, Xiang, 2022. "Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 622-654.
    11. Ben Hambly & Nikolaos Kolliopoulos, 2018. "Fast mean-reversion asymptotics for large portfolios of stochastic volatility models," Papers 1811.08808, arXiv.org, revised Feb 2020.
    12. Dai Pra, Paolo & Formentin, Marco & Pelino, Guglielmo, 2021. "A hierarchical mean field model of interacting spins," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 287-338.
    13. Michael B. Giles & Christoph Reisinger, 2012. "Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance," Papers 1204.1442, arXiv.org.
    14. Erny, Xavier, 2022. "Well-posedness and propagation of chaos for McKean–Vlasov equations with jumps and locally Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 192-214.
    15. Benazzoli, Chiara & Campi, Luciano & Di Persio, Luca, 2019. "ε-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    16. Rene Carmona & Kevin Webster, 2012. "High Frequency Market Making," Papers 1210.5781, arXiv.org.
    17. Bayraktar, Erhan & Wu, Ruoyu, 2023. "Graphon particle system: Uniform-in-time concentration bounds," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 196-225.
    18. Maroulas, Vasileios & Pan, Xiaoyang & Xiong, Jie, 2020. "Large deviations for the optimal filter of nonlinear dynamical systems driven by Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 203-231.
    19. Yulin Song, 2020. "Gradient Estimates and Exponential Ergodicity for Mean-Field SDEs with Jumps," Journal of Theoretical Probability, Springer, vol. 33(1), pages 201-238, March.
    20. Jun Moon & Wonhee Kim, 2020. "Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models," Mathematics, MDPI, vol. 8(10), pages 1-23, September.

    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:141:y:2021:i:c:p:197-244. 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.