The sector constants of continuous state branching processes with immigration |
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Authors: | Kenji Handa |
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Institution: | Department of Mathematics, Saga University, Saga 840-8502, Japan |
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Abstract: | Continuous state branching processes with immigration are studied. We are particularly concerned with the associated (non-symmetric) Dirichlet form. After observing that gamma distributions are only reversible distributions for this class of models, we prove that every generalized gamma convolution is a stationary distribution of the process with suitably chosen branching mechanism and with continuous immigration. For such non-reversible processes, the strong sector condition is discussed in terms of a characteristic called the Thorin measure. In addition, some connections with notion from non-commutative probability theory will be pointed out through calculations involving the Stieltjes transform. |
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