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Thread: Convergence in Probability

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    Convergence in Probability




    Hello all. I have a two statements. One says

    -\frac{1}{T}  \sum_{t=1}^T X_t \rightarrow a in probability as T \rightarrow \infty

    The other:

    -\frac{1}{g(T)}  \sum_{t=1}^g(T) X_t \rightarrow a in probability as T \rightarrow \infty for g N \rightarrow N such that g(T) \rightarrow \infty as T \rightarrow \infty

    Could you please tell me why are those two statements equivalent for random sequence X_{t}?
    Last edited by Dragan; 10-13-2014 at 04:01 PM. Reason: formatting

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    Re: Convergence in Probability

    Use "/" to close math tags (not "\")
    I don't have emotions and sometimes that makes me very sad.

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    Re: Convergence in Probability


    I think your formatting is still a bit off (recall in latex that if what you want in a superscript or above a summation is longer than one character you need to wrap it in curly braces).

    What does it mean for something to converge in probability? What does it mean for a sequence to go to infinity? Keep those statements in mind and write out what each of the two statements is saying.
    I don't have emotions and sometimes that makes me very sad.

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