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# Showing that X(t) is standard Brownian motion

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1. 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
2. (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
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 , for all s, and for , and B has continuous paths, the B is a Brownian motion.

Now do some computation.

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