Lévy-Khintchine Theorem

The Lévy-Khintchine theorem characterizes all possible probability distributions that can be represented as the limit of sums of independent, identically distributed random variables. It states that any such distribution's characteristic function can be written in a specific form involving three components: a drift term (deterministic trend), a Gaussian (normal) part (continuous fluctuations), and a jump part (sudden, discrete changes). This framework helps in modeling complex processes with both continuous variability and abrupt events, such as stock prices or natural phenomena, by providing a comprehensive mathematical description of their behavior.