On the Law of the Iterated Logarithm for m-dependent stationary random variables under sub-linear expectations

TL;DR

This paper extends the Law of the Iterated Logarithm to m-dependent stationary sequences within sub-linear expectation frameworks, providing new theoretical insights and necessary conditions for such stochastic processes.

Contribution

It introduces the first LIL results for m-dependent sequences under sub-linear expectations and establishes necessary conditions for their behavior.

Findings

Extended LIL to independent, non-identically distributed variables under sub-linear expectations

Established LIL for m-dependent stationary sequences

Provided necessary conditions for m-dependent sequences in sub-linear expectation spaces

Abstract

This paper explores the Law of the Iterated Logarithm (LIL) for $m$-dependent sequences under the framework of sub-linear expectations. We first extend existing LIL results to sequences of independent, non-identically distributed random variables under sub-linear expectations. This extension serves as a crucial intermediary step, facilitating the subsequent establishment of the LIL for $m$-dependent stationary sequences. On the other hand, we also establish necessary conditions for $m$-dependent sequences in sub-linear expectation spaces.