Uniqueness Problem for the Backward Differential Equation of a Continuous-State Branching Process  

作　　者：Pei Sen LI Zeng Hu LI 

机构地区：[1]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100872,P.R.China [2]School of Mathematical Sciences,Beijing Normal University,Beijing 100875,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第8期1825-1836,共12页数学学报（英文版）

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)。

摘　　要：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.

关 键 词：Continuous-state branching process MULTI-DIMENSIONAL backward differential equation stochastic equation generator 

分 类 号：O211.63[理学—概率论与数理统计]