IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v155y2023icp27-108.html
   My bibliography  Save this article

Large deviations for interacting multiscale particle systems

Author

Listed:
  • Bezemek, Z.W.
  • Spiliopoulos, K.

Abstract

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles’ positions in the combined limit as the number of particles grow to infinity and the time-scale separation parameter goes to zero. We make use of weak convergence methods providing a convenient representation for the large deviations rate function, which allow us to characterize the effective controlled mean field dynamics. In addition, we rigorously obtain equivalent non-variational representations for the large deviations rate function as introduced by Dawson–Gärtner.

Suggested Citation

  • Bezemek, Z.W. & Spiliopoulos, K., 2023. "Large deviations for interacting multiscale particle systems," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 27-108.
    • Handle: RePEc:eee:spapps:v:155:y:2023:i:c:p:27-108
    DOI: 10.1016/j.spa.2022.09.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922002010
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.09.010?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. Dupuis, Paul & Spiliopoulos, Konstantinos, 2012. "Large deviations for multiscale diffusion via weak convergence methods," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1947-1987.
    2. Ganguly, Arnab & Sundar, P., 2021. "Inhomogeneous functionals and approximations of invariant distributions of ergodic diffusions: Central limit theorem and moderate deviation asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 74-110.
    3. Jin Feng & Jean-Pierre Fouque & Rohini Kumar, 2010. "Small-time asymptotics for fast mean-reverting stochastic volatility models," Papers 1009.2782, arXiv.org, revised Aug 2012.
    4. Amarjit Budhiraja & Michael Conroy, 2022. "Empirical Measure and Small Noise Asymptotics Under Large Deviation Scaling for Interacting Diffusions," Journal of Theoretical Probability, Springer, vol. 35(1), pages 295-349, March.
    5. Veretennikov, A. Yu., 2000. "On large deviations for SDEs with small diffusion and averaging," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 69-79, September.
    6. Lacker, Daniel, 2015. "Mean field games via controlled martingale problems: Existence of Markovian equilibria," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2856-2894.
    7. Freidlin, Mark I. & Sowers, Richard B., 1999. "A comparison of homogenization and large deviations, with applications to wavefront propagation," Stochastic Processes and their Applications, Elsevier, vol. 82(1), pages 23-52, July.
    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. Konstantinos Spiliopoulos & Alexandra Chronopoulou, 2013. "Maximum likelihood estimation for small noise multiscale diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 16(3), pages 237-266, October.
    2. Kumar, Rohini & Popovic, Lea, 2017. "Large deviations for multi-scale jump-diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1297-1320.
    3. Antoine Jacquier & Konstantinos Spiliopoulos, 2018. "Pathwise moderate deviations for option pricing," Papers 1803.04483, arXiv.org, revised Dec 2018.
    4. Dupuis, Paul & Spiliopoulos, Konstantinos, 2012. "Large deviations for multiscale diffusion via weak convergence methods," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1947-1987.
    5. Solesne Bourguin & Thanh Dang & Konstantinos Spiliopoulos, 2023. "Moderate Deviation Principle for Multiscale Systems Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-57, March.
    6. Samuel Daudin, 2022. "Optimal Control of Diffusion Processes with Terminal Constraint in Law," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 1-41, October.
    7. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    8. Blessing, Jonas & Kupper, Michael & Nendel, Max, 2023. "Convergence of Infintesimal Generators and Stability of Convex Montone Semigroups," Center for Mathematical Economics Working Papers 680, Center for Mathematical Economics, Bielefeld University.
    9. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Small-time asymptotics for Gaussian self-similar stochastic volatility models," Papers 1505.05256, arXiv.org, revised Mar 2016.
    10. Jos'e E. Figueroa-L'opez & Ruoting Gong & Christian Houdr'e, 2013. "Third-Order Short-Time Expansions for Close-to-the-Money Option Prices under the CGMY Model," Papers 1305.4719, arXiv.org, revised Nov 2017.
    11. Popovic, Lea, 2019. "Large deviations of Markov chains with multiple time-scales," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3319-3359.
    12. Andrés Cárdenas & Sergio Pulido & Rafael Serrano, 2022. "Existence of optimal controls for stochastic Volterra equations," Working Papers hal-03720342, HAL.
    13. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    14. Bouveret, Géraldine & Dumitrescu, Roxana & Tankov, Peter, 2022. "Technological change in water use: A mean-field game approach to optimal investment timing," Operations Research Perspectives, Elsevier, vol. 9(C).
    15. Jos'e E. Figueroa-L'opez & Ruoting Gong & Christian Houdr'e, 2012. "High-order short-time expansions for ATM option prices of exponential L\'evy models," Papers 1208.5520, arXiv.org, revised Apr 2014.
    16. Antoine Jacquier & Alexandre Pannier, 2020. "Large and moderate deviations for stochastic Volterra systems," Papers 2004.10571, arXiv.org, revised Apr 2022.
    17. Cl´ement Manga & Alioune Coulibaly & Alassane Diedhiou, 2019. "On Jumps Stochastic Evolution Equations With Application of Homogenization and Large Deviations," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(2), pages 125-134, April.
    18. Fu, Guanxing & Horst, Ulrich, 2017. "Mean Field Games with Singular Controls," Rationality and Competition Discussion Paper Series 22, CRC TRR 190 Rationality and Competition.
    19. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2022. "A Unifying Framework for Submodular Mean Field Games," Center for Mathematical Economics Working Papers 661, Center for Mathematical Economics, Bielefeld University.
    20. Lingjiong Zhu, 2015. "Short maturity options for Azéma–Yor martingales," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-32, December.

    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:155:y:2023:i:c:p:27-108. 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.