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Inverting a characteristic function if the integral of the modulus of the cf is infinity
I'm reading a lecture slide that starts by asking if there's a way to invert a characteristic function $\psi_X$ if $\int|\psi_X(t)|~\mathrm{d}t = \infty$. From my reading, the slide then provides a ...
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Density from characteristic function: Durrett example 3.3.8 and 3.3.9
Letting $\varphi(t)$ be the characteristic function for the probability measure $\mu$, we know if $\int \left|\varphi(t)\right|dt < \infty$, then $\mu$ has density function
$$f(y) = \frac{1}{2\pi} \...
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