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Math Help - Constructing independent increments

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    Constructing independent increments

    How do I construct random variables increment (X(t+h) - X(t)) such that each increment is normally distributed with mean 0 and variance = h.

    I thought of using Ito's lemma and use standard normals with "e" mean 0 and variance 1. Use say 100 of them, and then the increments shall have mean 0 and variance h.

    However, the hint in the book talks about using compound poisson process or using uniform random variables. Any help appreciated.
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  2. #2
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    Quote Originally Posted by cryptic26 View Post
    How do I construct random variables increment (X(t+h) - X(t)) such that each increment is normally distributed with mean 0 and variance = h.

    I thought of using Ito's lemma and use standard normals with "e" mean 0 and variance 1. Use say 100 of them, and then the increments shall have mean 0 and variance h.

    However, the hint in the book talks about using compound poisson process or using uniform random variables. Any help appreciated.
    Anyone wishing to contribute to this thread can pm me. In light of another thread being completely vandalised by edit-deletes, I'm closing this thread.
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