We consider the decay parameter,invariant measures/vectors and quasi-stationary dis-tributions for 2-type Markov branching processes.Investigating such properties is crucial in realizing life period of branching model...We consider the decay parameter,invariant measures/vectors and quasi-stationary dis-tributions for 2-type Markov branching processes.Investigating such properties is crucial in realizing life period of branching models.In this paper,some important properties of the generating functions for 2-type Markov branching q-matrix are firstly investigated in detail.The exact value of the decay parameterλC of such model is given for the communicating class C=Z+2\0.It is shown that thisλC can be directly obtained from the generating functions of the corresponding q-matrix.Moreover,theλC-invariant measures/vectors and quasi-distributions of such processes are deeply considered.AλC-invariant vector for the q-matrix(or for the process)on C is given and the generating functions ofλC-invariant measures and quasi-stationary distributions for the process on C are presented.展开更多
A new class of branching models,the general collision branching processes with two parameters,is considered in this paper.For such models,it is necessary to evaluate the absorbing probabilities and mean extinction tim...A new class of branching models,the general collision branching processes with two parameters,is considered in this paper.For such models,it is necessary to evaluate the absorbing probabilities and mean extinction times for both absorbing states.Regularity and uniqueness criteria are firstly established.Explicit expressions are then obtained for the extinction probability vector,the mean extinction times and the conditional mean extinction times.The explosion behavior of these models is investigated and an explicit expression for mean explosion time is established.The mean global holding time is also obtained.It is revealed that these properties are substantially different between the super-explosive and sub-explosive cases.展开更多
基金supported by National Natural Science Foundation of China(Grant No.10771216)Project sponsored by Scientific Research Foundation for Returned Overseas Chinese Scholars,State Education Ministry(Grant No.[2007]1108)
文摘We consider the decay parameter,invariant measures/vectors and quasi-stationary dis-tributions for 2-type Markov branching processes.Investigating such properties is crucial in realizing life period of branching models.In this paper,some important properties of the generating functions for 2-type Markov branching q-matrix are firstly investigated in detail.The exact value of the decay parameterλC of such model is given for the communicating class C=Z+2\0.It is shown that thisλC can be directly obtained from the generating functions of the corresponding q-matrix.Moreover,theλC-invariant measures/vectors and quasi-distributions of such processes are deeply considered.AλC-invariant vector for the q-matrix(or for the process)on C is given and the generating functions ofλC-invariant measures and quasi-stationary distributions for the process on C are presented.
基金supported by National Natural Science Foundation of China (Grant No.10771216)Research Grants Council of Hong Kong (Grant No.HKU 7010/06P)Scientific Research Foundation for Returned Overseas Chinese Scholars,State Education Ministry of China (Grant No.[2007]1108)
文摘A new class of branching models,the general collision branching processes with two parameters,is considered in this paper.For such models,it is necessary to evaluate the absorbing probabilities and mean extinction times for both absorbing states.Regularity and uniqueness criteria are firstly established.Explicit expressions are then obtained for the extinction probability vector,the mean extinction times and the conditional mean extinction times.The explosion behavior of these models is investigated and an explicit expression for mean explosion time is established.The mean global holding time is also obtained.It is revealed that these properties are substantially different between the super-explosive and sub-explosive cases.
