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    I've been trying to solve this problem for ages and can't find any similar problems
    If B(t) is Standard Brownian Motion, how do I show that X(t) = (t+1) B(1/(t + 1)) − B(1) is Standard Brownian Motion for 0 ≤ t ≤ 1?
    I don't even know where to start
    Could anyone please help?
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    (Original post by Bruce Harrisface)
    I've been trying to solve this problem for ages and can't find any similar problems
    If B(t) is Standard Brownian Motion, how do I show that X(t) = (t+1) B(1/(t + 1)) − B(1) is Standard Brownian Motion for 0 ≤ t ≤ 1?
    I don't even know where to start
    Could anyone please help?
    So I hope that somewhere in your lecture notes you have a theorem like this:

    If B is a process such that all the finite-dimensional distributions are jointly normal, with  \mathbb{E}B_s = 0, for all s, and \mathrm{Cov}(B_s,B_t) = s for s \le t , and B has continuous paths, the B is a Brownian motion.

    Now do some computation.
 
 
 
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