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A stochastic process is a collection of random variables usually indexed by a totally ordered set.

1 vote

Lévy measure and Lévy process

Let us consider the one-dimensional case. By the Lévy-Khintchine formula, we have$$E(e^{i\theta X_1})= e^{-\phi(\theta)},$$ where $$\phi(\theta)=\int_{R}(1-e^{i\theta x}+i\theta x 1_{|x|<1})\nu(dx).$$ …
Peisen Li's user avatar