Kendall's Conjecture On One-order Q-process

This paper includes the following two parts: In part one the author introduces mainly the theory about Ray-Knight compactification and then shows some examples about Ray-Knight compactification; in part two the author simply introduces the Kendall's conjecture firstly, that is, the uniqueness of Q-process determined by 0~+-system. It's a very important problem in the research of Markov-chain. Many specialists in and abroad have made great contribution to it such as Reuter ,Hou Zhenting and so on. As the resolvent can be expressed by boundary process and excursion measure, the author in this paper has proved that 0~+-system determins Doob process, bilateral birth-and-death process and One-order Q-process uniquely. Therefore, it's very easy to see it's probabilitical meaning.