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
Polar set of Markov processes is an important concept in probabilistic potential theory, but it is not easy to judge the polarity of the sets. In this paper, we give some results which can be easily used to examine th...Polar set of Markov processes is an important concept in probabilistic potential theory, but it is not easy to judge the polarity of the sets. In this paper, we give some results which can be easily used to examine the polarity of the sets whenX t belongs to a special class of Levy processes. We also give a result about polar functions of symmetric stable processes.展开更多
By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in ...By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.展开更多
Let （Ω, F, P）=（[0, 1], [0, 1], μ）<sup>N</sup> （μ is the Lebesque measure, N={1, 2,…}）.{X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are independent random variabl...Let （Ω, F, P）=（[0, 1], [0, 1], μ）<sup>N</sup> （μ is the Lebesque measure, N={1, 2,…}）.{X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are independent random variables on （Ω, F, P） with X<sub>n</sub>（ω）=ω<sub>n</sub>, where ω=（ω<sub>1</sub>, ω<sub>2</sub>,…）. The {X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are almost surely distinct. Thus to almost all sample points ω there is a random partial order 【 of the integers given展开更多
X(t)(t∈[0,∞)) is a subordinator with its upper index β less than one, g(u) is the index function of X(t), and X[0,1]={x∈R:X(t)=x}, for some t∈ }. If (s)(s∈(0,1) ) is a measure function and h(s)=(s)g1s, then h-p(...X(t)(t∈[0,∞)) is a subordinator with its upper index β less than one, g(u) is the index function of X(t), and X[0,1]={x∈R:X(t)=x}, for some t∈ }. If (s)(s∈(0,1) ) is a measure function and h(s)=(s)g1s, then h-p(X)=0\ \ a.s. +∞\ a.s. according as ∫ 1 0φ 2(s)s d s<+∞, =+∞.The packing dimension of X(t) is the upper index β .展开更多
We introduce the results on the multifractal structure of the occupation measures of a Brownian Motion, a stable process, a general subordinator and a stochastic process derived from random reordering of the Cantor se...We introduce the results on the multifractal structure of the occupation measures of a Brownian Motion, a stable process, a general subordinator and a stochastic process derived from random reordering of the Cantor set. We also introduced an interesting and powerful technique to investigate the multifractal spectrum.展开更多
In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure...In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure.展开更多
We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps up...We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps upcrossing the level. By regarding the size of a jump as the birth site of a particle, we construct a branching particle system in which the particles undergo nonlocal branchings and deterministic spatial motions to the left on the positive half line. A particle is removed from the system as soon as it reaches the origin. Then a measure-valued Borel right Markov process can be defined as the counting measures of the particle system. Its total mass evolves according to a Crump- Mode-Jagers （CMJ） branching process and its support represents the residual life times of those existing particles. A similar result for spectrally negative Levy process is established by a time reversal approach. Properties of the measure- valued processes can be studied via the excursions for the corresponding Levy processes.展开更多
We consider an infinite capacity second-order fluid queue with subordinator input and Markovmodulated linear release rate. The fluid queue level is described by a generalized Langevin stochastic differential equation ...We consider an infinite capacity second-order fluid queue with subordinator input and Markovmodulated linear release rate. The fluid queue level is described by a generalized Langevin stochastic differential equation （SDE）. Applying infinitesimal generator, we obtain the stationary distribution that satisfies an integro-differential equation. We derive the solution of the SDE and study the transient level＇s convergence in distribution. When the coefficients of the SDE are constants, we deduce the system transient property.展开更多
In the paper, using Levy processes subordinated by ＇asymptotically self-similar activity time＇ pro- cesses with long-range dependence, we set up new asset pricing models. Using the different construction for gamma ...In the paper, using Levy processes subordinated by ＇asymptotically self-similar activity time＇ pro- cesses with long-range dependence, we set up new asset pricing models. Using the different construction for gamma （F） based ＇asymptotically self-similar activity time＇ processes with long-range dependence from Fin- lay and Seneta （2006） we extend the constructions for inverse-gamma and gamma based ＇asymptotically self- similar activity time＇ processes with integer-vMued parameters and long-range dependence in Heyde and Leo- nenko （2005） and Finlay and Seneta （2006） to noninteger-valued parameters.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）.
文摘Polar set of Markov processes is an important concept in probabilistic potential theory, but it is not easy to judge the polarity of the sets. In this paper, we give some results which can be easily used to examine the polarity of the sets whenX t belongs to a special class of Levy processes. We also give a result about polar functions of symmetric stable processes.
基金supported in part by the National Natural Science Foundation of China(1117126211171263)
文摘By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.
文摘Let （Ω, F, P）=（[0, 1], [0, 1], μ）<sup>N</sup> （μ is the Lebesque measure, N={1, 2,…}）.{X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are independent random variables on （Ω, F, P） with X<sub>n</sub>（ω）=ω<sub>n</sub>, where ω=（ω<sub>1</sub>, ω<sub>2</sub>,…）. The {X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are almost surely distinct. Thus to almost all sample points ω there is a random partial order 【 of the integers given
文摘X(t)(t∈[0,∞)) is a subordinator with its upper index β less than one, g(u) is the index function of X(t), and X[0,1]={x∈R:X(t)=x}, for some t∈ }. If (s)(s∈(0,1) ) is a measure function and h(s)=(s)g1s, then h-p(X)=0\ \ a.s. +∞\ a.s. according as ∫ 1 0φ 2(s)s d s<+∞, =+∞.The packing dimension of X(t) is the upper index β .
基金Supported by the National Natural Science Foundation of China
文摘We introduce the results on the multifractal structure of the occupation measures of a Brownian Motion, a stable process, a general subordinator and a stochastic process derived from random reordering of the Cantor set. We also introduced an interesting and powerful technique to investigate the multifractal spectrum.
文摘In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure.
基金Hui He wanted to thank Concordia University for his pleasant stay at Montreal where this work was done. The authors would like to thank Professor Wenming Hong for his enlightening discussion. They also would like to thank Amaury Lambert for suggesting the time reversal treatment of the model in Section 5. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11201030, 11371061）, the Fundamental Research Funds for the Central Universities （2013YB59）, and the Natural Sciences and Engineering Research Council of Canada.
文摘We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps upcrossing the level. By regarding the size of a jump as the birth site of a particle, we construct a branching particle system in which the particles undergo nonlocal branchings and deterministic spatial motions to the left on the positive half line. A particle is removed from the system as soon as it reaches the origin. Then a measure-valued Borel right Markov process can be defined as the counting measures of the particle system. Its total mass evolves according to a Crump- Mode-Jagers （CMJ） branching process and its support represents the residual life times of those existing particles. A similar result for spectrally negative Levy process is established by a time reversal approach. Properties of the measure- valued processes can be studied via the excursions for the corresponding Levy processes.
基金Supported by the National Natural Science Foundation of China(No.10726063)
文摘We consider an infinite capacity second-order fluid queue with subordinator input and Markovmodulated linear release rate. The fluid queue level is described by a generalized Langevin stochastic differential equation （SDE）. Applying infinitesimal generator, we obtain the stationary distribution that satisfies an integro-differential equation. We derive the solution of the SDE and study the transient level＇s convergence in distribution. When the coefficients of the SDE are constants, we deduce the system transient property.
基金supported by National Natural Science Foundation of China(Grant No.71271042)the Plan of Jiangsu Specially-Appointed Professors,the Jiangsu Hi-Level Innovative and Entrepreneurship Talent Introduction Plan and Major Program of Key Research Center in Financial Risk Management of Jiangsu Universities Philosophy Social Sciences(Grant No.2012JDXM009)
文摘In the paper, using Levy processes subordinated by ＇asymptotically self-similar activity time＇ pro- cesses with long-range dependence, we set up new asset pricing models. Using the different construction for gamma （F） based ＇asymptotically self-similar activity time＇ processes with long-range dependence from Fin- lay and Seneta （2006） we extend the constructions for inverse-gamma and gamma based ＇asymptotically self- similar activity time＇ processes with integer-vMued parameters and long-range dependence in Heyde and Leo- nenko （2005） and Finlay and Seneta （2006） to noninteger-valued parameters.
基金Supported by Applied Economics Base and the research fund of Zhejiang Sci-Tech University(15092100-Y)National Social Science Fund of China(15CJY009)Tianjin Philosophy and Social Sciences Planning Project(TJYYWT15-014)
