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Large deviations of mean-field stochastic differential equations with jumps

Author

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  • Cai, Yujie
  • Huang, Jianhui
  • Maroulas, Vasileios

Abstract

The mean-field stochastic differential equation (MFSDE) has found various applications in science and engineering. Here, we investigate a class of MFSDE with jumps, governed by a finite dimensional Brownian motion and a Poisson random measure. We study large deviation estimates of its path solution and our approach for verifying the large deviation principle is based on the weak convergence arguments.

Suggested Citation

  • Cai, Yujie & Huang, Jianhui & Maroulas, Vasileios, 2015. "Large deviations of mean-field stochastic differential equations with jumps," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 1-9.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:1-9
    DOI: 10.1016/j.spl.2014.08.010
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    References listed on IDEAS

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    1. Lambson, Val Eugene, 1984. "Self-enforcing collusion in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 34(2), pages 282-291, December.
    2. Maroulas, Vasileios & Xiong, Jie, 2013. "Large deviations for optimal filtering with fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2340-2352.
    3. Duan, Jinqiao & Millet, Annie, 2009. "Large deviations for the Boussinesq equations under random influences," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2052-2081, June.
    4. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    5. Sritharan, S.S. & Sundar, P., 2006. "Large deviations for the two-dimensional Navier-Stokes equations with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1636-1659, November.
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    1. 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.

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