柯氏向后微分方程组解的适定性

Properly posed problem of Kolmogorov backward differential equations

用泛函分析的理论和方法研究马尔可夫过程中生灭Q 矩阵的性质,证明在一定条件下生灭Q 矩阵生成一个线性算子C0半群,即此生灭Q 矩阵是某个C0半群的无穷小生成元.从而证明了生灭过程理论中的柯氏向后微分方程组解的存在性、唯一性和稳定性.

The property of birth and death Qmatrix in Markov processes is studied by using the theories and methods provided by functional analysis. It is proved that a birth and death Qmatrix generates a linear operator C0 semigroup, that is to say, the birth and death Qmatrix is the infinitesimal generator of the C0 semigroup. Therefore, the existence, uniqueness and stability of the solution of Kolmovgorov differential equations in Markov processes is verified.