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<p>In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of McKean-Vlasov stochastic partial differential equations with monotone coefficients. The main results can be applied to quasi-linear McKean-Vlasov equations such as distribution dependent stochastic porous media equation and stochastic <i>p</i>-Laplace equation. Our proof is based on the improved weak convergence approach proposed in (Liu, W.et al.: Potential Anal. <b>59</b>, 1141–1190 (2023)), which is specifically developed to handle the large deviation principle for distribution-dependent stochastic systems. Furthermore, by using the methodological strategy in (Wu, W. and Zhai, J.: SIAM J. Math. Anal. <b>56</b>, 1–42 (2024)), we employ the time discretization procedure and relative entropy estimates to successfully drop the compactness assumption of embedding in the Gelfand triple, enabling us to address both bounded and unbounded domains in applications.</p>

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McKean-Vlasov SPDEs Driven by Poisson Random Measure: Well-Posedness and Large Deviation Principle

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Yuhang Jiang,
  • Jinming Li,
  • Shihu Li

摘要

In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of McKean-Vlasov stochastic partial differential equations with monotone coefficients. The main results can be applied to quasi-linear McKean-Vlasov equations such as distribution dependent stochastic porous media equation and stochastic p-Laplace equation. Our proof is based on the improved weak convergence approach proposed in (Liu, W.et al.: Potential Anal. 59, 1141–1190 (2023)), which is specifically developed to handle the large deviation principle for distribution-dependent stochastic systems. Furthermore, by using the methodological strategy in (Wu, W. and Zhai, J.: SIAM J. Math. Anal. 56, 1–42 (2024)), we employ the time discretization procedure and relative entropy estimates to successfully drop the compactness assumption of embedding in the Gelfand triple, enabling us to address both bounded and unbounded domains in applications.