 Characteristic exponent of a Lévy process

ID: characteristic-exponent-of-a-levy-process

Use the convention

E e^{i u X_{t}} = e^{- t Ψ (u)} .

Then

Ψ

is the characteristic exponent of the Lévy process. Some authors instead write

e^{t ψ (u)}

, with

ψ = - Ψ

. The sign convention should always be specified. The Lévy–Khintchine formula describes all possible exponents.

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