Invariability of the Strong Markov Property in the Transformations of Dynkin

E. B. Dynkin in [2] has defined a large class of transformations of Markov processes. He calls processes obtained by these transformations $\widetilde X$ and $(\alpha,\xi)$-subprocesses of the process $X$. In this paper we prove that if the process $X$ is a strong Markov process, then, with some conditions imposed on $\alpha$ and $\xi$, the $(\alpha,\xi)$-subprocess will also be a strong Markov process. One special case of a $(\alpha,\xi)$ subprocess has been examined earlier by E. B. Dynkin in his book [1]. He proved in particular that the strong Markov property does not change in the formation of subprocesses. We show that the method he used for the special case can be carried over to the general case.