连续状态分枝过程的累积半群满足向后方程, 其 m 维版本被称为广义Riccati 方程. 该方程的解的存在唯一性与方程中的初值有关. 文献 [4] 提出方程解的存在唯一性当且仅当初值为零时解存在唯一, 即本文所述 R-S 命题. 本文对广义 Riccati 方程的相关结果进行了总结, 为证明 R-S 命题做出一定的尝试, 并在文中给出了一些可能的思路.

The cumulant semigroup of continuous-state branching processes satisfies the backward equation. The m dimensional versions of these equations are called the generalized Riccati equations. The existence and uniqueness of those equations depends on the initial value. In [4] the authors claim that the solution of the generalized Riccati equations exists and is unique if and only if the uniqueness holds when the initial value takes zero, that is, the R-S proposition described in this paper. We attempt to summarize the relevant results of the generalized Riccati equation and try to prove the R-S proposition, some possible ideas are given in this paper.