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MOMENTS OF CONTINUOUS-STATE BRANCHING PROCESSES IN LéVY RANDOM ENVIRONMENTS 被引量:1
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作者 Lina JI Xiangqi ZHENG 《Acta Mathematica Scientia》 SCIE CSCD 2019年第3期781-796,共16页
For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuo... For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions. 展开更多
关键词 Branching processes continuous-state MOMENTS RANDOM environment stochastic EQUATIONS
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Uniqueness Problem for the Backward Differential Equation of a Continuous-State Branching Process
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作者 Pei Sen LI Zeng Hu LI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第8期1825-1836,共12页
The distributional properties of a multi-dimensional continuous-state branching process are determined by its cumulant semigroup,which is defined by the backward differential equation.We provide a proof of the asserti... The distributional properties of a multi-dimensional continuous-state branching process are determined by its cumulant semigroup,which is defined by the backward differential equation.We provide a proof of the assertion of Rhyzhov and Skorokhod(Theory Probab.Appl.,1970)on the uniqueness of the solutions to the equation,which is based on a characterization of the process as the pathwise unique solution to a system of stochastic equations. 展开更多
关键词 continuous-state branching process MULTI-DIMENSIONAL backward differential equation stochastic equation generator
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Boundary Behaviors for a Continuous-state Nonlinear Neveu’s Branching Process
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作者 Lin Yu BAI Xu YANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第8期2005-2016,共12页
By generalizing a criterion of Mufa Chen for Markov jump processes,we establish the necessary and sufficient conditions for the extinction,explosion and coming down from infinity of a continuous-state nonlinear Neveu... By generalizing a criterion of Mufa Chen for Markov jump processes,we establish the necessary and sufficient conditions for the extinction,explosion and coming down from infinity of a continuous-state nonlinear Neveu’s branching process. 展开更多
关键词 continuous-state branching process nonlinear branching Neveu’s branching EXTINCTION explosion coming down from infinity
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Stochastic Equations for Two-type Continuous-state Branching Processes with Immigration 被引量:2
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作者 Ru Gang MA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第2期287-294,共8页
A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of t... A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of the solution is established. These results imply the existence and uniqueness of the strong solution of the stochastic equation system. 展开更多
关键词 continuous-state branching process IMMIGRATION stochastic integral equation comparison property strong solution
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Moments of Continuous-state Branching Processes with or Without Immigration 被引量:1
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作者 Li-na JI Zeng-hu LI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2020年第2期361-373,共13页
For a positive continuous function f satisfying some standard conditions,we study the f-moments of continuous-state branching processes with or without immigration.The main results give criteria for the existence of t... For a positive continuous function f satisfying some standard conditions,we study the f-moments of continuous-state branching processes with or without immigration.The main results give criteria for the existence of the f-moments.The characterization of the processes in terms of stochastic equations plays an essential role in the proofs. 展开更多
关键词 branching process continuous-state IMMIGRATION MOMENTS STOCHASTIC EQUATION
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Conditional limit theorems for critical continuous-state branching processes
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作者 REN YanXia YANG Ting ZHAO GuoHuan 《Science China Mathematics》 SCIE 2014年第12期2577-2588,共12页
We study the conditional limit theorems for critical continuous-state branching processes with branching mechanism Ф(λ) = λ 1+αL(1/λ), where (α∈ [0, 1] and L is slowly varying at co. We prove that if α ... We study the conditional limit theorems for critical continuous-state branching processes with branching mechanism Ф(λ) = λ 1+αL(1/λ), where (α∈ [0, 1] and L is slowly varying at co. We prove that if α ∈ (0, 1], there are norming constants Qt →0 (as t ↑ + ∞) such that for every x 〉 0, Px(QtXt ∈ · |Xt 〉 0) converges weakly to a non-degenerate limit. The converse assertion is also true provided the regularity of ψ at 0. We give a conditional limit theorem for the case α = 0. The limit theorems we obtain in this paper allow infinite variance of the branching process. 展开更多
关键词 continuous-state branching process conditional laws regular variation
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