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$X(t) := 0 \;\; (t \leq \tau),\;\; t - \tau\;\;(t \geq \tau)$ with $\tau$ exponentially distributed.

Then X has the Markov property but not Strong Markov Property. But why ???? Can someone kindly explain in words and maths why the strong markov property does not hold?

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    Hint: $X_{\tau+1}-X_\tau$ and $X_1$ have different distributions.2012-11-30

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