Getoor's conjecture that essentially all Lvy processes satisfy Hunt's hypothesis(H) is a longstanding open problem in potential theory. In the beginning of the paper, we summarize the main results obtained so ...Getoor's conjecture that essentially all Lvy processes satisfy Hunt's hypothesis(H) is a longstanding 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 Lvy 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
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 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 Lvy processes satisfy Hunt's hypothesis(H) is a longstanding 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 Lvy 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).
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.
