Getoor＇s conjecture that essentially all Levy processes satisfy Hunt＇s hypothesis （H） is a long- standing open problem in potential theory. In the beginning of the paper, we summarize the main results obtained so ...Getoor＇s conjecture that essentially all Levy processes satisfy Hunt＇s hypothesis （H） is a long- standing open problem in potential theory. In the beginning of the paper, we summarize the main results obtained so far for the problem. Then, we present two new necessary and sufficient conditions for the validity of （H）. Furthermore, we give applications of these new criteria. First, we give explicit constructions of Levy processes satisfying （H） in a context where previously known results could not be applied. Second, we show that a large class of pure jump subordinators can be decomposed into the summation of two independent subordinators such that both of them satisfy （H）.展开更多
Which Levy processes satisfy Hunt’s hypothesis(H)is a long-standing open problem in probabilistic potential theory.The study of this problem for one-dimensional Levy processes suggests us to consider(H)from the point...Which Levy processes satisfy Hunt’s hypothesis(H)is a long-standing open problem in probabilistic potential theory.The study of this problem for one-dimensional Levy processes suggests us to consider(H)from the point of view of the sum of Levy processes.In this paper,we present theorems and examples on the validity of(H)for the sum of two independent Levy processes.We also give a novel condition on the Levy measure which implies(H)for a large class of one-dimensional Levy processes.展开更多
The goal of this paper is threefold. First, we survey the existing results on Hunt’s hypothesis(H) for Markov processes and Getoor’s conjecture for Lévy processes. Second, we investigate(H)for multidimensional ...The goal of this paper is threefold. First, we survey the existing results on Hunt’s hypothesis(H) for Markov processes and Getoor’s conjecture for Lévy processes. Second, we investigate(H)for multidimensional Lévy processes from the viewpoint of projections. Third, we present a few open questions for further study.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11371191)Natural Science and Engineering Research Council of Canada (Grant No. 311945-2013)
文摘Getoor＇s conjecture that essentially all Levy processes satisfy Hunt＇s hypothesis （H） is a long- standing open problem in potential theory. In the beginning of the paper, we summarize the main results obtained so far for the problem. Then, we present two new necessary and sufficient conditions for the validity of （H）. Furthermore, we give applications of these new criteria. First, we give explicit constructions of Levy processes satisfying （H） in a context where previously known results could not be applied. Second, we show that a large class of pure jump subordinators can be decomposed into the summation of two independent subordinators such that both of them satisfy （H）.
基金work was supported by National Natural Science Foundation of China(Grant No.11771309)Natural Science and Engineering Research Council of Canada(Grant No.311945-2013)the Fundamental Research Funds for the Central Universities of China。
文摘Which Levy processes satisfy Hunt’s hypothesis(H)is a long-standing open problem in probabilistic potential theory.The study of this problem for one-dimensional Levy processes suggests us to consider(H)from the point of view of the sum of Levy processes.In this paper,we present theorems and examples on the validity of(H)for the sum of two independent Levy processes.We also give a novel condition on the Levy measure which implies(H)for a large class of one-dimensional Levy processes.
基金Supported by National Natural Science Foundation of China(Grant Nos.11771309 and 11871184)Natural Sciences and Engineering Research Council of Canada(Grant No.4394-2018)。
文摘The goal of this paper is threefold. First, we survey the existing results on Hunt’s hypothesis(H) for Markov processes and Getoor’s conjecture for Lévy processes. Second, we investigate(H)for multidimensional Lévy processes from the viewpoint of projections. Third, we present a few open questions for further study.
