I have to prove that $[p,p] = t$ with $p$ defined in the following way:
$$ N_u = \sum_{i=1}^n(B_t^i)^2 $$ $$ p = \sum_{i=1}^n \int_0^t \frac{B_u^i dB_u^i}{\sqrt{N_u}}$$
Theoretically i know that Brownian motion of all independent n- dimensional Brownian motion will be zero for above term and i will be only left with dependent BM, but how to mathematically denote these steps?