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The enhanced Sanov theorem and propagation of chaos

Author

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  • Deuschel, Jean-Dominique
  • Friz, Peter K.
  • Maurelli, Mario
  • Slowik, Martin

Abstract

We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the (k-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies a propagation of chaos result in a space of rough paths and allows for a robust analysis of the particle system and its McKean–Vlasov type limit, as shown in two corollaries.

Suggested Citation

  • Deuschel, Jean-Dominique & Friz, Peter K. & Maurelli, Mario & Slowik, Martin, 2018. "The enhanced Sanov theorem and propagation of chaos," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2228-2269.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:7:p:2228-2269
    DOI: 10.1016/j.spa.2017.09.010
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    References listed on IDEAS

    as
    1. Ledoux, M. & Qian, Z. & Zhang, T., 2002. "Large deviations and support theorem for diffusion processes via rough paths," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 265-283, December.
    2. Wang, Ran & Wang, Xinyu & Wu, Liming, 2010. "Sanov's theorem in the Wasserstein distance: A necessary and sufficient condition," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 505-512, March.
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