Let B be a separable real Banach space and m be a positive measure on B. In this paper, we will establish the Beurling-Deny formulae of the Dirichlet forms on L~2(B, dm).
The uniqueness of the Beurling-Deny first formula in quasi-regular Dirichlet spaces is verified in terms of the strictly strong local property. An extension of the Beurling-Deny second formula is obtained in infinite...The uniqueness of the Beurling-Deny first formula in quasi-regular Dirichlet spaces is verified in terms of the strictly strong local property. An extension of the Beurling-Deny second formula is obtained in infinite dimensional spaces.展开更多
In this paper,we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric space...In this paper,we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces.Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.展开更多
A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approx...A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approximation sequency satisfies the conditon. Furthermore, conditions for the Mosco limit of a sequence of symmetric (strictly strong) local quasi-regular Dirichlet forms to be (strictly strong) local are also presented. This paper extends the results of [1] from regular Dirichlet space to quasi-regular Dirichlet space.展开更多
文摘Let B be a separable real Banach space and m be a positive measure on B. In this paper, we will establish the Beurling-Deny formulae of the Dirichlet forms on L~2(B, dm).
文摘The uniqueness of the Beurling-Deny first formula in quasi-regular Dirichlet spaces is verified in terms of the strictly strong local property. An extension of the Beurling-Deny second formula is obtained in infinite dimensional spaces.
基金supported by National Natural Science Foundation of China(Grant No.10721101)National Basic Research Program of China(Grant No.2006CB805900)+1 种基金Key Lab of Random Complex Structures and Data Science,Chinese Academy of Sciences(Grant No.2008DP173182)Sino-Germany IGK Project
文摘In this paper,we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces.Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.
文摘A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approximation sequency satisfies the conditon. Furthermore, conditions for the Mosco limit of a sequence of symmetric (strictly strong) local quasi-regular Dirichlet forms to be (strictly strong) local are also presented. This paper extends the results of [1] from regular Dirichlet space to quasi-regular Dirichlet space.
