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Math Help - Comparison of stochastic processes at a random time 2

  1. #1
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    Comparison of stochastic processes at a random time 2

    Let X_t and Y_t, t \in \mathbb{N}, be two discrete-time Markov chains such that Pr(X_t\ge x) \le Pr(Y_t\ge x), for all x. Let T be a non-negative random variable in \mathbb{N} (T may depend on X and Y).

    Is it true that Pr(X_T\ge x) \le Pr(Y_T\ge x) ?

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  2. #2
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    Good morning. Please can you help me to solve this exercise?. I must to use limiting distribution and change of variable. Thank you my friend.
    Let Yn denote the nth order statistic, with Yn=qXn:n – ln(n), of a random sample X1,X2,…………..Xn from a exponential distribution Xi~exp(q). Find the limiting distribution of Yn.
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  3. #3
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    I think that still conditioning over T it should be ok, right?
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  4. #4
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    yes i would think so.
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