Given a sequence of random variables $(X_n)_n$ (fulfilling the Markov property) and a stopping time $\tau$ such that $P(\tau < \infty)=1$, we have that $P(X_{\tau+1}=x_1,X_{\tau+2}=x_2,...|X_{\tau}=x) = P(X_{1}=x_1,X_{2}=x_2,...|X_{0}=x)$. I don't understand where the stopping time comes into play. Why is it not equivalent to say that $\forall n \in \mathbb{N}: P(X_{n+1}=x_1,X_{n+2}=x_2,...|X_{n}=x) = P(X_{1}=x_1,X_{2}=x_2,...|X_{0}=x)$?
2026-04-12 05:38:56.1775972336
Strong Markov property and its meaning
112 Views Asked by user66906 https://math.techqa.club/user/user66906/detail AtRelated Questions in REAL-ANALYSIS
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