Case 1: Function is in terms of X (Brownian Motion)
Case 1a: F = F(X)
dF = \frac{1}{2}\frac{d^2F}{dX^2}dt + \frac{dF}{dX}dX
Case 1b: F = F(t, X)
dF = \left(\frac{\partial F}{\partial t} + \frac{1}{2}\frac{\partial^2 F}{\partial X^2} \right)dt + \frac{\partial F}{\partial X}dX
Case 2: Function is in terms of Z
dZ = a(Z, t) dt + b(Z, t) dX
Case 2a: F = F(Z)
dF = \left(a\frac{dF}{dZ} + \frac{1}{2}b^2\frac{d^2F}{dZ^2} \right)dt + \left(b\frac{dF}{dZ} \right)dX
Case 2b: F = F(t, Z)
dF = \left(\frac{\partial F}{\partial t} + a\frac{\partial F}{\partial Z} + \frac{1}{2}b^2\frac{\partial^2 F}{\partial Z^2} \right)dt + \left(b\frac{\partial F}{\partial Z} \right)dX
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