In this paper, the authors study the ω-transience and ω-recurrence for Levy processes with any weight function ω, give a relation between ω-recurrence and the last exit times. As a special case, the polynomial rec...In this paper, the authors study the ω-transience and ω-recurrence for Levy processes with any weight function ω, give a relation between ω-recurrence and the last exit times. As a special case, the polynomial recurrence and polynomial transience are also studied.展开更多
The authors investigate the α-transience and α-recurrence for random walks and Levy processes by means of the associated moment generating function, give a dichotomy theorem for not one-sided processes and prove tha...The authors investigate the α-transience and α-recurrence for random walks and Levy processes by means of the associated moment generating function, give a dichotomy theorem for not one-sided processes and prove that the process X is quasisymmetric if and only if X is not α-recurrent for all α＜ 0 which gives a probabilistic explanation of quasi-symmetry, a concept originated from C. J. Stone.展开更多
It is skowed that if the first exit distribution leaving any ball from the center is theuniform distribution on the sphere, then the Levy process is a scaled Brownian motion.The paper also gives a characterization of ...It is skowed that if the first exit distribution leaving any ball from the center is theuniform distribution on the sphere, then the Levy process is a scaled Brownian motion.The paper also gives a characterization of a continuous Hunt process by the first exitdistribution from any ball.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
In 1979,Jurek gave a characterization of the moment of a full operator-stable μ by eigenvalues of exponent matrix of μ. Here, a characterization of the moment of Lévy measure (restricted on a neighbor of 0) of ...In 1979,Jurek gave a characterization of the moment of a full operator-stable μ by eigenvalues of exponent matrix of μ. Here, a characterization of the moment of Lévy measure (restricted on a neighbor of 0) of a full operator-stable μ by eigenvalues of exponent matrix of μ is given.展开更多
In the present paper the transformation of symmetric Markov processes by symmetric martingale multiplicative functionals is studied and the corresponding Dirichlet form is formulated.
基金Project supported by the National Natural Science Foundation of China (No.10271109).
文摘In this paper, the authors study the ω-transience and ω-recurrence for Levy processes with any weight function ω, give a relation between ω-recurrence and the last exit times. As a special case, the polynomial recurrence and polynomial transience are also studied.
基金Project supported by the National Natural Science Foundation of China (No. 10271109).
文摘The authors investigate the α-transience and α-recurrence for random walks and Levy processes by means of the associated moment generating function, give a dichotomy theorem for not one-sided processes and prove that the process X is quasisymmetric if and only if X is not α-recurrent for all α＜ 0 which gives a probabilistic explanation of quasi-symmetry, a concept originated from C. J. Stone.
基金Project supported by the National Natural Science Foundation of China (No.10271109)
文摘It is skowed that if the first exit distribution leaving any ball from the center is theuniform distribution on the sphere, then the Levy process is a scaled Brownian motion.The paper also gives a characterization of a continuous Hunt process by the first exitdistribution from any ball.
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In 1979,Jurek gave a characterization of the moment of a full operator-stable μ by eigenvalues of exponent matrix of μ. Here, a characterization of the moment of Lévy measure (restricted on a neighbor of 0) of a full operator-stable μ by eigenvalues of exponent matrix of μ is given.
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.
