Infinite Divisibility of Probability Distributions on the Real Line reassesses classical theory and presents new developments, while focusing on divisibility with respect to convolution or addition of independent random variables. This definitive, example-rich text supplies approximately 100 examples to correspond with all major chapter topics and reviews infinite divisibility in light of the central limit problem. It contrasts infinite divisibility with finite divisibility, discusses the preservation of infinite divisibility under mixing for many classes of distributions, and investigates self-decomposability and stability on the nonnegative reals, nonnegative integers, and the reals.
Infinitely divisible distributions on the nonnegative integers; infinitely divisible distributions on the nonnegative reals; infinitely divisible distributions on the real line; self-decomposability and stability; infinite divisibility and mixtures;infinite divisibility in stochastic processes. Appendices: prerequisites from probability and analysis; list of well-known distributions; notations and conventions.