3. Define the stochastic process X(t) = (1 /t)B((a^2)t), t 0.

Show that X(t) is also a standard Brownian Motion, for any a > 0. Hint: verify that the properties in the definition of a BM hold. Also check that the covariance structure is the same, i.e. compute Cov(X(ti), X(tj )) for any ti , tj in some partition chosen a priori, i.e. = {0 = t0, t1, ..., tn = T}. Moreover, you may use Theorem 4.6.4 (Levy, one dimension) from the textbook.