Suppose Z(t) is the standard Brownian process, show that the following processes defined by are also Brownian
Question:
Suppose Z(t) is the standard Brownian process, show that the following processes defined by
are also Brownian processes.
To show that Xi(t) is a Brownian process, i = 1, 2, 3, it suffices to show that
is normally distributed with zero mean, and
Also, the increments over disjoint time intervals are independent and Xi(0) = 0.
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