This paper is concerned with coupled linear forward-backward stochastic differential equations(FBSDEs,for short).When the homogeneous coefficients are deterministic(the non-homogeneous coefficients can be random),we o...This paper is concerned with coupled linear forward-backward stochastic differential equations(FBSDEs,for short).When the homogeneous coefficients are deterministic(the non-homogeneous coefficients can be random),we obtain an L^(P)-result(p>2),including the existence and uniqueness of the p-th power integrable solution,a p-th power estimate,and a related continuous dependence property of the solution on the coefficients,for coupled linear FBSDEs in the monotonicity framework over large time intervals.In order to get rid of the stubborn constraint commonly existing in the literature,i.e.,the Lipschitz constant of σ with respect to z is very small,we introduce a linear transformation to overcome the difficulty on small intervals,and then"splice"the L^(P)-results obtained on many small intervals to yield the desired one on a large interval.展开更多
We introduce a special tracial Rokhlin property for unital C~＊-algebras. Let A be a unital tracial rank zero C~＊-algebra（or tracial rank no more than one C~＊-algebra）. Suppose that α ： G → Aut（A） is an actio...We introduce a special tracial Rokhlin property for unital C~＊-algebras. Let A be a unital tracial rank zero C~＊-algebra（or tracial rank no more than one C~＊-algebra）. Suppose that α ： G → Aut（A） is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~＊-algebra. Then, the crossed product C~＊-algebra C~＊（G, A, α） has tracia rank zero（or has tracial rank no more than one）. In fact,we get a more general results.展开更多
In this short note,we give a proof of our partial C^0-estimate for Kähler-Einstein metrics.Our proof uses a compactness theorem of Cheeger-Colding-Tian and L^2-estimate for∂^--operator.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11871310,12271304 and 11971262)the Natural Science Foundation of Shandong Province(Grant No.ZR2020MA014)。
文摘This paper is concerned with coupled linear forward-backward stochastic differential equations(FBSDEs,for short).When the homogeneous coefficients are deterministic(the non-homogeneous coefficients can be random),we obtain an L^(P)-result(p>2),including the existence and uniqueness of the p-th power integrable solution,a p-th power estimate,and a related continuous dependence property of the solution on the coefficients,for coupled linear FBSDEs in the monotonicity framework over large time intervals.In order to get rid of the stubborn constraint commonly existing in the literature,i.e.,the Lipschitz constant of σ with respect to z is very small,we introduce a linear transformation to overcome the difficulty on small intervals,and then"splice"the L^(P)-results obtained on many small intervals to yield the desired one on a large interval.
文摘We introduce a special tracial Rokhlin property for unital C~＊-algebras. Let A be a unital tracial rank zero C~＊-algebra（or tracial rank no more than one C~＊-algebra）. Suppose that α ： G → Aut（A） is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~＊-algebra. Then, the crossed product C~＊-algebra C~＊（G, A, α） has tracia rank zero（or has tracial rank no more than one）. In fact,we get a more general results.
文摘In this short note,we give a proof of our partial C^0-estimate for Kähler-Einstein metrics.Our proof uses a compactness theorem of Cheeger-Colding-Tian and L^2-estimate for∂^--operator.
