On Markov Processes with Right-Deterministic Germ Fields

Abstract

Given a Hunt process $X(t)$, we investigate the consequences of the assumption that $\mathscr{G}(T+) = \sigma(X(T))$ for every finite stopping time $T$, where $\mathscr{G}(T+) = \bigcap_{\varepsilon > 0} \mathscr{F}^0\lbrack T, T + \varepsilon)$. Such processes constitute a simple extension of the right-continuous Markov chains without instantaneous states.