论文标题
在$ l_ {d} $的随机方程式上
On stochastic equations with drift in $L_{d}$
论文作者
论文摘要
对于$ \ m athbb {r}^{d} $中的随机方程，在$ l_ {d}中漂移，讨论了几个结果，例如存在薄弱的解决方案，相应的马尔可夫过程的存在，Aleksandrov的存在，Aleksandrov类型的绿色功能估算了它们的功能，从而使其在$ d/d/fable的功能中产生了$ d/d/d/fab的能力，该构成了$ d/d/fabip $ d/d/fabip $ d/d/fabip $ d/fabip。可以在更高程度上总结一下Fanghua Lin类型估计值，这是$ W^{2} _ {P} $ - 完全非线性椭圆方程的理论，Green的功能在$ A级$ A _ {\ iffty} $的Muckenhoupt和其他一些结果的事实中。
For Itô stochastic equations in $\mathbb{R}^{d}$ with drift in $L_{d}$ several results are discussed such as the existence of weak solutions, the existence of the corresponding Markov process, Aleksandrov type estimates of their Green's functions, which yield their summability to the power of $d/(d-1)$, the Fabes-Stroock type estimates which show that Green's functions are summable to a higher degree, the Fanghua Lin type estimates, which are one of the main tools in the $W^{2}_{p}$-theory of fully nonlinear elliptic equations, the fact that Green's functions are in the class $A_{\infty}$ of Muckenhoupt and a few other results.
