Here is a multidimensional version of Levy’s theorem. Let {F t } be a filtration satisfying the usual conditions. Suppose   is a d-dimensional process such that each component M i is a continuous...

Here is a multidimensional version of Levy’s theorem. Let {F_t} be a filtration satisfying the usual conditions. Suppose
  is a d-dimensional process such that each component Mⁱ
is a continuous martingale with respect to
  Suppose that

if i = j. Prove that
  is a d-dimensional Brownian motion.