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
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
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
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
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
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
基金supported by the National Natural Science Foundation of China(11531001)
文摘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.
基金supported by the National Key R&D Program of China(Grant No.2020YFA0712900)the National Natural Science Foundation of China(Grant No.12271029)。
文摘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.
基金Supported by NSFC(Grant No.12061004)NSF of Ningxia(Grant No.2021AAC02018)+2 种基金the Fundamental Research Funds for the Central Universities,North Minzu University(Grant No.2020KYQD17)Major research project for North Minzu University(Grant No.ZDZX201902)the Construction Project of First-Class Disciplines in Ningxia Higher Education(Grant No.NXYLXK2017B09)。
文摘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.
基金supported by the National Natural Science Foundation of China(No.11531001 and No.11626245).
文摘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.
文摘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.
基金supported by National Natural Science Foundation of China(Grant Nos.11271030 and 11128101)Specialized Research Fund for the Doctoral Program of Higher Education and China Postdoctoral Science Foundation(Grant No.2013M541061)
文摘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.
