Actually, what i am trying to check is the result for the expression of the characteristic function of the Z variable in terms in terms of the X variable, that is using the inverse Fourier transform.
If i implement the formula in Matlab using FFT, then the results don't match (direct formula vs...
Indeed this is what my final goal is: calculate the characteristic function of Z in terms of the characteristic function of X.
The problem is that in my case X has a more complicated distribution, namely being the solution of stochastic differential equation for a double exponential jump...
Homework Statement
In order to determine the characteristic function of a random variable defined by: Z = max(X,0) where X is any continuous rv, i need to prove that:
F_{l,v}(g(l))=[ \phi_{X}(u+v)\phi_{X}(v) ] / (iv)
where F_{l,v}(g(l)) is the Fourier transform of g(l) and...