Suppose I have a multidimensional brownian motion $W=\{W_t\}$. Why is the following true:
$\langle W^k,W^l\rangle_t = \delta_{k,l}t$
where $W^k$ denotes the k-th coordinate, $\langle \cdot,\cdot\rangle$ denotes the bracket process and as usual $\delta_{k,l}$ the kronecker symbol.
cheers
math