On a quantum martingale convergence theorem

Polya’s Urn and the Martingale Convergence Theorem

This paper is about Polya’s Urn and the Martingale Convergence Theorem. I will start with the formal definition, followed by a simple example of martingale and the basic properties of martingale. Then I will explain the Polya’s Urn model and how it contributes to proving the Martingale Convergence Theorem. Finally, I will give a full proof of the Martingale Convergence Theorem.

Algorithmic randomness for Doob's martingale convergence theorem in continuous time

We study Doob’s martingale convergence theorem for computable continuous time martingales on Brownian motion, in the context of algorithmic randomness. A characterization of the class of sample points for which the theorem holds is given. Such points are given the name of Doob random points. It is shown that a point is Doob random if its tail is computably random in a certain sense. Moreover, D...

A Martingale Decomposition Theorem

A Martingale Central Limit Theorem

We present a proof of a martingale central limit theorem (Theorem 2) due to McLeish (1974). Then, an application to Markov chains is given.

A Martingale System Theorem for Stock Investments

In tlus paper we consider an investment strategy called dollar-cast-averaging (DCA). It is well known that the argument in favor of DCA is flawed: an investor cannot get something for nothing. Probabilists have made tltis type of flaw precise with theorems like the optional sampling theorem or, more generally, the martingale system theorem (see e.g. [4]). It is interesting that the usual martin...