# stochastic calculus and multidimentional itos lemma

I am considering a number of assets (N) in a portfolio. each asset follows a geometric Brownian motion process therefore the stochastic differential equation is dS(i) = S(i)μdt + S(i)σdX(i). The price changes are correlated as measured by the linear correlation coefficients rho(ij) . how do i deduce the multi-dimensional Ito's Lemma to write down the SDE for F(S1; S2; : : : ; SN) in the most compact form possible (with clear drift and diffusion terms) including crorrelation between dX(i)dX(j) that is rho(i,j)dt?

• Hi user161976, welcome to Quant.SE! Please add the self-study tag if it applies. Can you tell us what you've found already and where exactly your stuck? – Bob Jansen Aug 19 '15 at 6:15
• thanks Bob, I wrote down the 2-dimensional ito's lemma for the SDE and deduced the drift and diffusion for the process. I would appreciate if you could help me deduce it for N number of stocks. – user161976 Aug 20 '15 at 6:34