見本路に依存するジャンプ拡散過程の漸近挙動

取决于样本路径的跳跃扩散过程的渐近行为

• 批准号: 22KF0158
• 负责人: 謝 賓
• 金额: $ 1.41万
• 依托单位: Shinshu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2023
• 资助国家: 日本
• 起止时间: 2023-03-08 至 2024-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22KF0158/
• 关键词: p-Laplacian; delay; BDG inequality; anisotropic; distribution dependent; transformation; approximation; SPDEs; alpha-stable; Euler-Maruyama

We mainly studied stochastic anisotropic stochastic partial differential equations and approximation of path-distribution dependent SDEs driven by alpha-stable noise.The details are following:(1) We study well-posedness for stochastic anisotropic p-Laplacian reaction-diffusion equation with delay under non-Lipschitz conditions and stochastic anisotropic Navier-Stokes equations with delay. It is worth pointing out that, in contrast to the exist results, the essential difficulty in this work is how to discuss the problem of the uniqueness of solutions for anisotropic SPFDEs under non-Lipschitz condition, other than dealing with the anisotropic one. Under weaker conditions than those imposed in existing literature we show the well-posedness of stochastic partial functional differential equations with anisotropic exponents. Based on the result obtained, we explore the well-posedness of two kinds of typical examples.(2) We show via interacting particle systems an approximation issue on a class of path-distribution dependent SDEs driven by alpha-stable noise, where the drift is singular. The Zvonkin-type approach based on the existing literature does not work for the case of SDEs with multiplicative noises, although the jump diffusion processes can be estimated. Our work involves primarily two parts. The first part shows the well-posedness of path-distribution dependent stochastic differential equations and the corresponding stochastic interacting particle systems. The second part shows approximations of these path-distribution dependent stochastic differential equations.

We mainly studied stochastic anisotropic stochastic partial differential equations and approximation of path-distribution dependent SDEs driven by alpha-stable noise.The details are following:(1) We study well-posedness for stochastic anisotropic p-Laplacian reaction-diffusion equation with delay under non-Lipschitz conditions and stochastic anisotropic Navier-Stokes equations with delay.值得指出的是，与存在结果相比，这项工作的基本困难是如何讨论在非lipschitz条件下各向异性SPFDE的溶液唯一性的问题，而不是处理各向异性。在现有文献中所施加的条件下，我们表明了与各向异性指数的随机部分功能微分方程的适当性。基于获得的结果，我们探索了两种典型示例的良好性。（2）我们通过相互作用的粒子系统显示在一类依赖于alpha stable噪声的路径分布依赖性的SDE上，其中漂移是单数。基于现有文献的ZVONKIN类型方法对于带有乘法噪声的SDE不起作用，尽管可以估算跳跃扩散过程。我们的工作主要涉及两个部分。第一部分显示了依赖于路径分布的随机微分方程和相应的随机相互作用粒子系统的良好性。第二部分显示了这些路径分布依赖性随机微分方程的近似值。