STOPPING TIME CHANGES OF TIME HOMOGENEOUS MARKOV PROCESSES（Ⅰ）

Let X=\left(\Omega, \mathscrF, \mathscrF_t, X_t, \theta_t, P^x, T\right) be a time homogeneous Markov process with state space \left(E_\mathrmA, \mathscrE_\mathrmA\right) and \tau=\left(\tau_t\right) be an ( \mathscrF_t ) stopping time change (i. e. each \tau_t is an ( \mathscrF_t ) stopping time and " s \geqslant t \Rightarrow \tau_s \geqslant \tau_t "). Then X^\tau=\left(\Omega, \mathscrF^2, \mathscrF_\tau_t, X_\tau_t, \theta_\tau_t, P^x, T\right) is called a \tau-transformation of X. This paper makes a systematic study of invariant properties of Markov processes by stopping time changes. General stopping time ohanges of general Markov processes are considered and various conditions are given, under which the new process X^\tau preserves corresponding properties (e.g. Markov property, strong Markov property, strong Feller property, normal property, complete property and standard property etc.) of the original process X.