The author investigates the relationships of some potential objects for a right Markov process and the same objects for the Girsanov transformed process induced byα-excessive function including Revuz measures, energy...The author investigates the relationships of some potential objects for a right Markov process and the same objects for the Girsanov transformed process induced byα-excessive function including Revuz measures, energy functionals, capacities and Lévy systems in this paper.展开更多
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
LET X=（X<sub>t</sub>,P<sup>x</sup>） be a right Markov process with state space （E,ε）, semigroup （P<sub>1</sub>） andresolvent （U<sup>q</sup>）. As in ref.[1, 2], ...LET X=（X<sub>t</sub>,P<sup>x</sup>） be a right Markov process with state space （E,ε）, semigroup （P<sub>1</sub>） andresolvent （U<sup>q</sup>）. As in ref.[1, 2], we denote by Exc<sup>q</sup>（X ）, Dis<sup>q</sup>（X） and Con<sup>q</sup>（X） thecones of excessive, dissipative, conservative measures of X, respectively, and by S<sup>q</sup>（X） thecone of excessive functions of X. By convention we drop the superscript q when it is zero. LetMF be the set of all exact multiplicative functional of X. For any given M∈MF, writeE<sub>M</sub>:= {x∈E:P<sup>M<sub>0</sub> = 1</sup> = 1} and S<sub>M</sub>: = inf} t】0: M<sub>1</sub>= 0 } for the set of展开更多
We study the SchrSdinger equation （q -￡）u ＋μu = f, where ￡ is the generator of a Borel right process and μ is a signed measure on the state space. We prove the existence and uniqueness results in Lp, 1 ≤p 〈∞...We study the SchrSdinger equation （q -￡）u ＋μu = f, where ￡ is the generator of a Borel right process and μ is a signed measure on the state space. We prove the existence and uniqueness results in Lp, 1 ≤p 〈∞ . Since we consider measures μcharging no polar set, we have to use new tools： the Revuz formula with fine versions and the appropriate Revuz correspondence, the perturbation （subordination） operators （in the sense of G Mokobodzki） induced by the regular strongly supermedian kernels. We extend the results on the SchrSdinger equation to the case of a strongly continuous sub-Markovian resolvent of contractions on Lp. If the measure μ is positive then the perturbed process solves the martingale problem for ￡- μ and its transition semigroup is given by the Feynman-Kac formula associated with the left continuous additive functional having μ as Revuz measure.展开更多
The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2] and improves their result by a diffe...The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2] and improves their result by a different approach.展开更多
n this paper we introduce homogeneous multiplicative functionals of Levy processes and investigate their bivariate Revuz measures. We also prove that the sector condition will be inherited by suly-Lvy processes throug...n this paper we introduce homogeneous multiplicative functionals of Levy processes and investigate their bivariate Revuz measures. We also prove that the sector condition will be inherited by suly-Lvy processes through the killing transformation.展开更多
基金supported by the National Natural Science Foundation of China(No.11201221)the Natural Science Foundation of Jiangsu Province(No.BK2012468)
文摘The author investigates the relationships of some potential objects for a right Markov process and the same objects for the Girsanov transformed process induced byα-excessive function including Revuz measures, energy functionals, capacities and Lévy systems in this paper.
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LET X=（X<sub>t</sub>,P<sup>x</sup>） be a right Markov process with state space （E,ε）, semigroup （P<sub>1</sub>） andresolvent （U<sup>q</sup>）. As in ref.[1, 2], we denote by Exc<sup>q</sup>（X ）, Dis<sup>q</sup>（X） and Con<sup>q</sup>（X） thecones of excessive, dissipative, conservative measures of X, respectively, and by S<sup>q</sup>（X） thecone of excessive functions of X. By convention we drop the superscript q when it is zero. LetMF be the set of all exact multiplicative functional of X. For any given M∈MF, writeE<sub>M</sub>:= {x∈E:P<sup>M<sub>0</sub> = 1</sup> = 1} and S<sub>M</sub>: = inf} t】0: M<sub>1</sub>= 0 } for the set of
基金Supported by Deutsche Forschungsgemeinschaft (Project GZ: 436 RUM 113/23/0-1)the Romanian Ministry of Education, Research and Youth (PN Ⅱ Program, Project 373/2007, CNCSIS code ID 209)
文摘We study the SchrSdinger equation （q -￡）u ＋μu = f, where ￡ is the generator of a Borel right process and μ is a signed measure on the state space. We prove the existence and uniqueness results in Lp, 1 ≤p 〈∞ . Since we consider measures μcharging no polar set, we have to use new tools： the Revuz formula with fine versions and the appropriate Revuz correspondence, the perturbation （subordination） operators （in the sense of G Mokobodzki） induced by the regular strongly supermedian kernels. We extend the results on the SchrSdinger equation to the case of a strongly continuous sub-Markovian resolvent of contractions on Lp. If the measure μ is positive then the perturbed process solves the martingale problem for ￡- μ and its transition semigroup is given by the Feynman-Kac formula associated with the left continuous additive functional having μ as Revuz measure.
文摘The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2] and improves their result by a different approach.
文摘n this paper we introduce homogeneous multiplicative functionals of Levy processes and investigate their bivariate Revuz measures. We also prove that the sector condition will be inherited by suly-Lvy processes through the killing transformation.
