集值马尔可夫过程及其存在性

如同马尔可夫过程在随机过程理论中的重要性一样，集值马尔可夫过程在集值随机过程理论中也是非常重要的。但由于种种原因，到目前为止，集值马尔可夫过程能见到的研究成果还不多见，就连它的定义，至今还没有统一的处理，使研究工作感到困难。从最直观的角度给出集植马尔可夫过程的定义，在此基础上，证明了它的一系列定义的等价性，从而对这类过程的本质有较为完整的认识。类似于经典情形一样，引进了转移函数和集值齐次马尔可夫过程的概念。运用柯尔莫哥洛夫定理，讨论了集值齐次马尔可夫过程的判定定理。在上述讨论的基础上，证明了齐次集值马尔可夫过程的存在性。

Set -Valued Markov Processes and its Existence

Set-Valued Markov process plays an important role in the set-valued stochastic processes, as Markov porcess is important in the stochastic processes. For some reasons, the research on set-valued Markov processes is not enough, and its definition is not uniform, which makes the deeper research very difficult. This article proves the equivalent of all kinds of conditions from the simple definition, thus getting a general knowledge about the essential of this processes.Transit-function and definition of the homogeneous set-valaed Markov processes are introduced and the resolation theorem is discussed. Based on A.N. Kolmogroo theory, the existence of the homogeneous set-valued Markov processes is proved.