In the present paper the transformation of symmetric Markov processes by symmetric martingale multiplicative functionals is studied and the corresponding Dirichlet form is formulated.
LetXbe an m s ymmetric Markov process andMa multiplicative functional ofXsuch that theMsubprocess ofXis alsom-symmetric.The author characterizes the Dirichlet form associated with the subprocess in terms of that assoc...LetXbe an m s ymmetric Markov process andMa multiplicative functional ofXsuch that theMsubprocess ofXis alsom-symmetric.The author characterizes the Dirichlet form associated with the subprocess in terms of that associated withXand the bivariate Revuz measure ofM.展开更多
The author introduces a notion of subordination for symmetric Dirichlet forms and proves that the subordination is actually equivalent to the killing transformation by multiplicative functionals in the theory of symm...The author introduces a notion of subordination for symmetric Dirichlet forms and proves that the subordination is actually equivalent to the killing transformation by multiplicative functionals in the theory of symmetric Markov processes. This also gives a way to characterize bivariate smooth measures.展开更多
We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the p...We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the process, while the precise expression of the （L^2-）generator of the Dirichlet form associated with the process is used to obtain the lower bounds.展开更多
The authors introduce concepts of even and odd additive functionals and prove that an even martingale continuous additive functional of a symmetric Markov process vanishes identically.A representation for symmetric s...The authors introduce concepts of even and odd additive functionals and prove that an even martingale continuous additive functional of a symmetric Markov process vanishes identically.A representation for symmetric super-martingale multiplicative functionals are also given.展开更多
Let X be a Markov process, which is assumed to be associated with a (non-symmetric) Dirichlet form (E,D(E)) on L2 (E;m).?For , the extended Dirichlet space, we give necessary and sufficient conditions for a multiplica...Let X be a Markov process, which is assumed to be associated with a (non-symmetric) Dirichlet form (E,D(E)) on L2 (E;m).?For , the extended Dirichlet space, we give necessary and sufficient conditions for a multiplicative functional to be a positive local martingale.展开更多
基金in partby the National Natural Science Founda-tion of China(1 950 1 0 36)
文摘In the present paper the transformation of symmetric Markov processes by symmetric martingale multiplicative functionals is studied and the corresponding Dirichlet form is formulated.
文摘LetXbe an m s ymmetric Markov process andMa multiplicative functional ofXsuch that theMsubprocess ofXis alsom-symmetric.The author characterizes the Dirichlet form associated with the subprocess in terms of that associated withXand the bivariate Revuz measure ofM.
文摘The author introduces a notion of subordination for symmetric Dirichlet forms and proves that the subordination is actually equivalent to the killing transformation by multiplicative functionals in the theory of symmetric Markov processes. This also gives a way to characterize bivariate smooth measures.
基金Supported partly by Grand-in-Aid for Scientific Research (C)
文摘We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the process, while the precise expression of the （L^2-）generator of the Dirichlet form associated with the process is used to obtain the lower bounds.
基金Project supported by the National Natural Science Foundation of China.
文摘The authors introduce concepts of even and odd additive functionals and prove that an even martingale continuous additive functional of a symmetric Markov process vanishes identically.A representation for symmetric super-martingale multiplicative functionals are also given.
文摘Let X be a Markov process, which is assumed to be associated with a (non-symmetric) Dirichlet form (E,D(E)) on L2 (E;m).?For , the extended Dirichlet space, we give necessary and sufficient conditions for a multiplicative functional to be a positive local martingale.
