Exchangeability, functional equations, and characterizations (Q2734977)

This is a survey paper on exchangeable sequences of random variables and random elements, reviewing recent literature, connecting recent results and discussing their proofs (some of them sketched). Some new results are included. NEWLINENEWLINENEWLINESubjects: De Finetti's theorem (conditional i.i.d. for infinite sequences), its generalizations and related inequalities from which solutions of generalized Choquet-Deny equations are derived. NEWLINENEWLINENEWLINEApplication: Proof of the strong renewal theorem. The above theory is applied to characterization of probability distributions, e.g. (conditional) convolution type distributions, stable and elliptically symmetric distributions and characterizations by records and order statistics. NEWLINENEWLINENEWLINEOther applications: Storage theory and damage models.NEWLINENEWLINEFor the entire collection see [Zbl 0961.60001].