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Does anybody have the solution of that problem, please? I don't understand the relation between random variables $X$ and $T$.

Regards

Edit :

Thank you for the comments.

Let me first apologize for asking such an imprecise question.

My level in probability theory is not good.

The problem is about stopping time. We have $X$ which is a stochastic process, and $T$ which is a random time. $T$ is $\mathcal{F}_t^{X}$-measurable. How can we show that if $X(\omega) = X(\omega')$ we necessarily have $T(\omega) = T(\omega')$? I am trying to understand the problem, but I just don't understand the relation between $X$ and $T$. That's why I do not have any clear solution idea to propose.

Regards

mStudent
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    This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level. (And please make the question self-contained.) – Did Jan 17 '14 at 10:39
  • You need to post the question with your attempt for us to help you. – Lost1 Jan 17 '14 at 11:57
  • Maybe this will help: http://math.stackexchange.com/questions/625580/equality-of-value-implies-equality-of-stopping-time –  Jan 17 '14 at 13:14
  • Thank you Byron, it helps a lot! – mStudent Jan 17 '14 at 13:38
  • what you write here is still wrong. $X$ is NOT a random variable. $X$ is a process. – Lost1 Jan 17 '14 at 13:42
  • Thank you Lost1. Correction made. – mStudent Jan 17 '14 at 13:54
  • The assumption is probably that $X_s(\omega)=X_s(\omega')$ for every $s\leqslant t$. – Did Jan 17 '14 at 15:01

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