The perturbation of semigroup by a multiplicative functional with bounded variation is investigated in the frame of weak duality. The strong continuity and Schrodinger type equation of the perturbated semigroup are di...The perturbation of semigroup by a multiplicative functional with bounded variation is investigated in the frame of weak duality. The strong continuity and Schrodinger type equation of the perturbated semigroup are discussed. A few switching identities and formulae conerning dual additive functionals and Revuz measures are given.展开更多
设ξ=（∈ι,Πx）是Rd中的右过程,令 （?）（x,z）=a（x）z+b（x）z2+ integral from n =1 to ∞(e-uz-1+uz)nx（du）, x∈Rd,z∈R+,（1）考虑下面Dirichlet问题 Av（x）-（?）（x,u（x））=0,x ∈ D,（2） （?） u（x）=f（a）,a∈...设ξ=（∈ι,Πx）是Rd中的右过程,令 （?）（x,z）=a（x）z+b（x）z2+ integral from n =1 to ∞(e-uz-1+uz)nx（du）, x∈Rd,z∈R+,（1）考虑下面Dirichlet问题 Av（x）-（?）（x,u（x））=0,x ∈ D,（2） （?） u（x）=f（a）,a∈（?）Dr,（3）这里D是Rd中有界区域,（?）Dr表示（?）D中正规点全体,且A是ξ关于D的特征算子. 我们用M表示（?）（Rd）上的有限测度全体,用（?）表示M上由fB（μ）=μ（B）,B∈（?）产生的σ-代数.本文中τ都表示开集D的首出时.根据Dynkin存在取值于（M,（?））的具有参数（ξ,（?））的超过程 X={Xt,Xτ,Pμ,μ∈ M}.Dynkin在文献[1]中证明了如果ξ是光滑一致椭圆算子,关于x局部Lipshitz连续,公式 v（x）=- log Pδexp（-（f, Xτ））（4）是方程（2）Dirichlet问题的唯一解.本文将上面结果推广到一些一般型条件（底过程不一定连续）.展开更多
In the paper,we obtain the SRC lifting of a right continuous, left upper semi-continuous random process on a Loeb space.And show the existence of S-optimal stopping of an internal process,construct the S-optimal stopp...In the paper,we obtain the SRC lifting of a right continuous, left upper semi-continuous random process on a Loeb space.And show the existence of S-optimal stopping of an internal process,construct the S-optimal stopping. Finally we prove the fact that the standard part of the S-optimal stopping of a SRC lifting is the optimal stopping of the corresponding standard process,which generalizes the conclusions in [8]on a Loeb space.展开更多
基金Project supported in part by the National Natural Science Foundation of China (No.19501035).
文摘The perturbation of semigroup by a multiplicative functional with bounded variation is investigated in the frame of weak duality. The strong continuity and Schrodinger type equation of the perturbated semigroup are discussed. A few switching identities and formulae conerning dual additive functionals and Revuz measures are given.
文摘In the paper,we obtain the SRC lifting of a right continuous, left upper semi-continuous random process on a Loeb space.And show the existence of S-optimal stopping of an internal process,construct the S-optimal stopping. Finally we prove the fact that the standard part of the S-optimal stopping of a SRC lifting is the optimal stopping of the corresponding standard process,which generalizes the conclusions in [8]on a Loeb space.
