I need to know how to come up with a guess function where I can apply itos formula on and hence solve the SDE. Is there any systematic method?
For example: $$dY(t)= 3Y(t)^{1/3}dt + 3Y(t)^{2/3}dB(t)$$ My teacher uses the guess function $$X(t)=Y(t)^{1/3}$$
Like, I don't know where this guess function comes at all. I have many of these kind of SDE:s and I want a method (systematic one) on how I can obtain these guess functions. I know the rest of the machinery.
Similiarly, why does the SDE
$$dX(t)=ax(t)dt+bx(t)db(t)$$ have the guess function $$Y(t)=ln(x(t))$$
I just don't get it where it comes from... Big thanks in advance, been searching all over the internet.