拓展里奇流是Hamilton里奇流的推广,具有强烈的几何和物理背景。本文考虑紧致的拓展里奇流的共轭热方程,用初等和直接的方法证明了其基本解的Harnack不等式。The extended Ricci flow is a generalization of the Hamiltonian Ricci flo...拓展里奇流是Hamilton里奇流的推广,具有强烈的几何和物理背景。本文考虑紧致的拓展里奇流的共轭热方程,用初等和直接的方法证明了其基本解的Harnack不等式。The extended Ricci flow is a generalization of the Hamiltonian Ricci flow with a strong geometric and physical background. In this paper, we consider the conjugate heat equation for the compact extended Ricci flow and prove Harnack’s inequality for its fundamental solution by elementary and direct methods.展开更多
In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H...In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H is supposed to be in(1/2, 1). As a direct application, the strong Feller property is presented.展开更多
针对一类带泊松跳的随机微分方程,在一些合理的条件假设下研究了该类方程解的半群11():[()]x t t tP f x E f X I≤的Harnack不等式和Log-Harnack不等式问题.首先建立了两类半群之间的关系,同时使用耦合方法,结合Girsanov定理、H?lder...针对一类带泊松跳的随机微分方程,在一些合理的条件假设下研究了该类方程解的半群11():[()]x t t tP f x E f X I≤的Harnack不等式和Log-Harnack不等式问题.首先建立了两类半群之间的关系,同时使用耦合方法,结合Girsanov定理、H?lder不等式、Young不等式以及Ito公式,先后获得了Harnack和Log-Harnack的2种不等式.展开更多
文摘拓展里奇流是Hamilton里奇流的推广,具有强烈的几何和物理背景。本文考虑紧致的拓展里奇流的共轭热方程,用初等和直接的方法证明了其基本解的Harnack不等式。The extended Ricci flow is a generalization of the Hamiltonian Ricci flow with a strong geometric and physical background. In this paper, we consider the conjugate heat equation for the compact extended Ricci flow and prove Harnack’s inequality for its fundamental solution by elementary and direct methods.
基金The research of L.Yan was partially supported bythe National Natural Science Foundation of China (11971101)The research of Z.Chen was supported by National Natural Science Foundation of China (11971432)+3 种基金the Natural Science Foundation of Zhejiang Province (LY21G010003)supported by the Collaborative Innovation Center of Statistical Data Engineering Technology & Applicationthe Characteristic & Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University-Statistics)the First Class Discipline of Zhejiang-A (Zhejiang Gongshang University-Statistics)。
文摘In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H is supposed to be in(1/2, 1). As a direct application, the strong Feller property is presented.
文摘针对一类带泊松跳的随机微分方程,在一些合理的条件假设下研究了该类方程解的半群11():[()]x t t tP f x E f X I≤的Harnack不等式和Log-Harnack不等式问题.首先建立了两类半群之间的关系,同时使用耦合方法,结合Girsanov定理、H?lder不等式、Young不等式以及Ito公式,先后获得了Harnack和Log-Harnack的2种不等式.
