見本路に依存するジャンプ拡散過程の漸近挙動

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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.