I have the problem: Let (B^1_t,B^2_t)_{t\ge0} be a 2-dimensional Brownian motion. Show that the process X_t=(B^1_t,B_t^2,\frac{1}{2}\int_0^tB_s^1dB_s^2-B_s^2dB_s^1)_{t\ge0} solves the stochastic differential equation that may be written dX_t=V_1(X_t)\circ dB^1_t+V_2(X_t)\circ dB_t^2 where V_1,V_2 are 2 vector fields to be computed.

Any idea?