Reverse-martigale Characterisations of Symmetric Laws

Specialeforsvar ved Martin Bladt

Titel: Reverse-martingale Characterisations of Symmetric Laws 

Abstract: This dissertation investigates the relationship between reverse-martingales and symmetric random objects. The fact that the empirical distributions of an exchangeable sequence form a reverse martingale is a well-know result. The converse statement is proved, under the additional assumption of stationarity. A similar reverse-martingale for separately exchangeable matrices is found and marginal characterisations are considered. In order to put the previous results in context, some of the classic theory of exchangeable objects is provided in detail. More importantly and in the same vein, results on martingale and reverse-martingale characterisations by Kallenberg are reproduced, yielding some useful methods of proof.

Vejleder:  Steffen Lauritzen
Censor:   Alexander Sokol, Nordea