MATH 545, Stochastic Calculus Problem set 2
d) X t = ˆ tB 1=t; if t>0 0; if t= 0;1 By Theorem 3.3 in [Klebaner]: X t is a mean zero gaussian process with covariance structure Cov(X s;X t) = min(s;t).Because rescaling time and brownian motion paths does not affect the mean of the process not its Gaussian structure, the first two points above are trivial.
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