Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition

TL;DR

This paper derives precise asymptotic results for large deviations, the law of large numbers, and the central limit theorem in chains with unbounded variable length memory satisfying the Cramer condition.

Contribution

It provides the first exact asymptotic formulas for these probabilistic properties in chains with unbounded variable length memory under the Cramer condition.

Findings

Exact asymptotics for large deviations

Strong law of large numbers established

Central limit theorem proved

Abstract

Here we obtain the exact asymptotics for large and moderate deviations, strong law of large numbers and central limit theorem for chains with unbounded variable length memory.