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
It is showed that if the first exit distribution leaving any ball from the center is the uniform distribution on the sphere, then the Levy process is a scaled Brownian motion.The paper also gives a characterization of...It is showed that if the first exit distribution leaving any ball from the center is the uniform 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 exit distribution from any ball.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
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Project supported by the National Natural Science Foundation of China (No.10271109)
文摘It is showed that if the first exit distribution leaving any ball from the center is the uniform 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 exit distribution from any ball.
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.
