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Math Help - mean square limit

  1. #1
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    mean square limit

    I'm spending hours trying to develop and prove the mean-square-limit.

    Does anyone know where I could find an exhaustive and detailed proof online?

    I would really appreciate!

    Here is the concept:

    Assume the finite time t is sliced into n identical partitions.
    Define tj as the time up to the end of the j-th partition.

    <br />
t_j= \frac{jt}{n}<br />

    The mean-square-limit sais that
    <br />
\lim_{n \rightarrow \infty} E\left[ \left( \sum_{j=1}^n\ (X(t_j)-X(t_{j-1}))^2-t \right)^2 \right] = 0<br />

    where X's are brownian motions and E is the expectation.

    Limit is zero because (developing and resolving) E=O(1/n)
    Last edited by CaptainBlack; January 24th 2008 at 05:27 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by paolopiace View Post
    I'm spending hours trying to develop and prove the mean-square-limit.

    Does anyone know where I could find an exhaustive and detailed proof online?

    I would really appreciate!

    Here is the concept:

    Assume the finite time t is sliced into n identical partitions.
    Define tj as the time up to the end of the j-th partition.

    <br />
t_j= \frac{jt}{n}<br />

    The mean-square-limit sais that
    <br />
\lim_{n \rightarrow \infty} E[(\sum_{j=1}^n\ (X(t_j)-X(t_{j-1}))^2-t)^2] = 0<br />

    where X's are brownian motions and E is the expectation.

    Limit is zero because (developing and resolving) E=O(1/n)
    Check your brackets, they don't match.

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Check your brackets, they don't match.

    RonL
    Brackets are correct...
    It's the E of the {square of the [sum of the (deltas squared) minus time]}
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