I have to find the Doob Meyer decomposition for the following process:
$Y_t=e^{(1+B_t^2)}$
I think that the method is to derive with the Ito's formula the process and I've obtained:
$dY_t=2B_te^{(1+B_t^2)}dB_t+e^{1+B_t^2}(1+2B^2_t)dt$
I want the process in an explicit mode (not with the integral). Is there a general method to do this with other process?