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
In this article, we mainly discuss some potential theory in the framework of right Markov processes. We introduce the concept of α-excessive function, α-recurrence and α-transience for right processes with α ≤ 0,...In this article, we mainly discuss some potential theory in the framework of right Markov processes. We introduce the concept of α-excessive function, α-recurrence and α-transience for right processes with α ≤ 0, and give a thorough investigation.展开更多
Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and characterize them by pot...Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and characterize them by potentials, excessive functions, first hitting times and last exit times of the process. We also study the properties of recurrent states.展开更多
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.
文摘In this article, we mainly discuss some potential theory in the framework of right Markov processes. We introduce the concept of α-excessive function, α-recurrence and α-transience for right processes with α ≤ 0, and give a thorough investigation.
文摘Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and characterize them by potentials, excessive functions, first hitting times and last exit times of the process. We also study the properties of recurrent states.
