In this note, we obtain a sufficient and necessary condition for a set in an abstract Winner space （X, H, μ） to be relatively compact in L^2（X, μ）. Meanwhile, we give a sufficient condition for relative compactn...In this note, we obtain a sufficient and necessary condition for a set in an abstract Winner space （X, H, μ） to be relatively compact in L^2（X, μ）. Meanwhile, we give a sufficient condition for relative compactness in L^P（X, μ） for p〉1. We also provide an example of Da Prato-Malliavin Nualart to show the result.展开更多
Let (H, B, u) be an abstract Wiener space. New spaces of test functionals and distributions having kernels of the chaos decomposition in (Hn,n】0) are constructed. Their counterparts over Rm are completely characteriz...Let (H, B, u) be an abstract Wiener space. New spaces of test functionals and distributions having kernels of the chaos decomposition in (Hn,n】0) are constructed. Their counterparts over Rm are completely characterized in terms of the H-transform.展开更多
In this paper, the dimensional-free Harnack inequalities are established on infinite-dimen- sional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhle...In this paper, the dimensional-free Harnack inequalities are established on infinite-dimen- sional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important quantities in one inequality, the relative entropy ＂H＂, Wasserstein distance ＂W＂, and Fisher information ＂T＂.展开更多
This paper deals with the approximate solution of the Fredholm equation u TKu = f of the second kind from a probabilistic point of view. With Wiener typemeasures on the set of kernels and free terms we determine stati...This paper deals with the approximate solution of the Fredholm equation u TKu = f of the second kind from a probabilistic point of view. With Wiener typemeasures on the set of kernels and free terms we determine statistical features of the approximation process, i.e., the most likely rate of convergence and the dominating individual behavior. The analysis carried out for a kind of Galerkin-like method.展开更多
The authors construct a solution U_t(x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a s...The authors construct a solution U_t(x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity,namely one-fold differentiability.Besides,the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained.展开更多
Concerning the study of Banach support for the sample space of a random process, the idea can go back to the penetrating investigation of R. Dudley, V.N. Sudaso and X. Fernique, about Gaussian cylindrical measure. Gro...Concerning the study of Banach support for the sample space of a random process, the idea can go back to the penetrating investigation of R. Dudley, V.N. Sudaso and X. Fernique, about Gaussian cylindrical measure. Gross, Ito, Sato and J. Kuelbs have investigated Banach support of a measure which, however, considers essentially Gaussian measure and proves that there exists Banach support for ordinary Gaussian measures. The abstract Wieber space introduced by Gross plays an important role in the study of Gaussian process. The ergodic and quasi-invariant measures investigated in this note are much wider than the abstract Wiener spaces, and the results obtained are stronger than the展开更多
The aim of this paper is to show Cauchy-Kowalevski and Holmgren type theorems with an infinite number of variables. We adopt von Koch and Hilbert’s definition of analyticity of functions as monomial expansions. Our C...The aim of this paper is to show Cauchy-Kowalevski and Holmgren type theorems with an infinite number of variables. We adopt von Koch and Hilbert’s definition of analyticity of functions as monomial expansions. Our Cauchy-Kowalevski type theorem is derived by modifying the classical method of majorants.Based on this result, by employing some tools from abstract Wiener spaces, we establish our Holmgren type theorem.展开更多
基金supported by NSF(No.10301011)of China Project 973
文摘In this note, we obtain a sufficient and necessary condition for a set in an abstract Winner space （X, H, μ） to be relatively compact in L^2（X, μ）. Meanwhile, we give a sufficient condition for relative compactness in L^P（X, μ） for p〉1. We also provide an example of Da Prato-Malliavin Nualart to show the result.
文摘Let (H, B, u) be an abstract Wiener space. New spaces of test functionals and distributions having kernels of the chaos decomposition in (Hn,n】0) are constructed. Their counterparts over Rm are completely characterized in terms of the H-transform.
基金Supported by National Natural Science Foundation of China （Grant No. 10721091） and the 973-Project （Grant No. 2006CB805901）
文摘In this paper, the dimensional-free Harnack inequalities are established on infinite-dimen- sional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important quantities in one inequality, the relative entropy ＂H＂, Wasserstein distance ＂W＂, and Fisher information ＂T＂.
文摘This paper deals with the approximate solution of the Fredholm equation u TKu = f of the second kind from a probabilistic point of view. With Wiener typemeasures on the set of kernels and free terms we determine statistical features of the approximation process, i.e., the most likely rate of convergence and the dominating individual behavior. The analysis carried out for a kind of Galerkin-like method.
基金Project supported by the National Natural Science Foundation of China(Nos.11171358,11026202,11101441)the Doctor Fund of Ministry of Education(Nos.20100171110038,20100171120041)the Natural Science Foundation of Guangdong Province(No.S2012040007458)
文摘The authors construct a solution U_t(x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity,namely one-fold differentiability.Besides,the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained.
基金Project supported by the National Natural Science Foundation of China
文摘Concerning the study of Banach support for the sample space of a random process, the idea can go back to the penetrating investigation of R. Dudley, V.N. Sudaso and X. Fernique, about Gaussian cylindrical measure. Gross, Ito, Sato and J. Kuelbs have investigated Banach support of a measure which, however, considers essentially Gaussian measure and proves that there exists Banach support for ordinary Gaussian measures. The abstract Wieber space introduced by Gross plays an important role in the study of Gaussian process. The ergodic and quasi-invariant measures investigated in this note are much wider than the abstract Wiener spaces, and the results obtained are stronger than the
基金supported by National Natural Science Foundation of China(Grant No.11501384)supported by National Natural Science Foundation of China(Grant No.11221101)+1 种基金the NSFC-CNRS Joint Research Project(Grant No.11711530142)the Program for Changjiang Scholars and Innovative Research Team in University from the Chinese Education Ministry(Grant No.IRT 16R53)
文摘The aim of this paper is to show Cauchy-Kowalevski and Holmgren type theorems with an infinite number of variables. We adopt von Koch and Hilbert’s definition of analyticity of functions as monomial expansions. Our Cauchy-Kowalevski type theorem is derived by modifying the classical method of majorants.Based on this result, by employing some tools from abstract Wiener spaces, we establish our Holmgren type theorem.
