Suppose X and Y evolve according to:
dXt= (2 + 5t + Xt)dt + 3 dz_1t
dYt= 4Ytdt + 8Ytdz_1t + 6dz_2t
where z_1t and z_2t are Brownian motions with (dz_1t )(dz_2t )=0.1dt
Can you give me some starting point how to transform the equations to the initial SDE in order to apply the Ito's lemma?
$$ df = \frac{\partial f}{\partial t}dt + \frac{\partial f}{\partial X_t}dX_t + \frac{1}{2}\frac{\partial^2 f}{\partial X_t^2}dX_t^2 $$ That's Ito's
thus $$ dX_t^4 = \frac{\partial }{\partial X_t}\left(X_t^4\right)dX_t + \frac{1}{2}\frac{\partial^2 }{\partial X_t^2}\left(X_t^4\right)dX_t^2 $$ Compute the partials first then use the fact that $\left(dz_t^1\right)^2 = dt$ to compute the sde. Then do a similar process for all the above, except you have to use the modified Ito for multivariable when you have to it for $f\left(X_t,Y_t\right)$.