Nonconventional Large Deviations Theorems

TL;DR

This paper develops large deviations theorems for sums involving nonconventional processes, including Markov chains and dynamical systems, expanding the theoretical understanding of rare events in complex stochastic models.

Contribution

It introduces large deviations results for nonconventional sums in Markov processes and dynamical systems, broadening the scope of classical large deviations theory.

Findings

Large deviations principles established for Markov processes under Doeblin condition

Results extended to dynamical systems like subshifts and hyperbolic transformations

Provides theoretical foundation for analyzing rare events in complex systems

Abstract

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.