Characteristic Functions and the Fourier Inversion Formula

Students often struggle to see the relationship between the characteristic function and the Moment Generating Function (MGF). Remember that while the MGF

M_X(t)

may not exist for many distributions, the characteristic function

\varphi_X(t)

always exists and is well-behaved due to the boundedness of

e^{itX}

Institutional Reference: Advanced Stochastic Processes

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