Combining losing games into a winning game

TL;DR

This paper extends Parrondo's paradox to regime switching random walks in random environments, providing a full characterization of their complex asymptotic behaviors using advanced mathematical tools.

Contribution

It introduces a novel model combining regime switching with random environments and offers a comprehensive analysis of its asymptotic properties.

Findings

The model exhibits richer asymptotic behaviors than traditional random walks.

The behavior is characterized using dimensions of subspaces from Oseledec's theorem.

The paradoxical effect is explained by the influence of the random environment.

Abstract

Parrondo's paradox is extended to regime switching random walks in random environments. The paradoxical behavior of the resulting random walk is explained by the effect of the random environment. Full characterization of the asymptotic behavior is achieved in terms of the dimensions of some random subspaces occurring in Oseledec's theorem. The regime switching mechanism gives our models a richer and more complex asymptotic behavior than the simple random walks in random environments appearing in the literature, in terms of transience and recurrence.