{"ID":2857885,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.07757","arxiv_id":"2510.07757","title":"Statistical properties of Markov shifts (part I)","abstract":"We prove central limit theorems, Berry-Esseen type theorems, almost sure invariance principles, large deviations and Livsic type regularity for partial sums of the form $S_n=\\sum_{j=0}^{n-1}f_j(...,X_{j-1},X_j,X_{j+1},...)$, where $(X_j)$ is an inhomogeneous Markov chain satisfying some mixing assumptions and $f_j$ is a sequence of sufficiently regular functions. Even though the case of non-stationary chains and time dependent functions $f_j$ is more challenging, our results seem to be new already for stationary Markov chains. They also seem to be new for non-stationary Bernoulli shifts (that is when $(X_j)$ are independent but not identically distributed). This paper is the first one in a series of two papers. In \\cite{Work} we will prove local limit theorems including developing the related reduction theory in the sense of \\cite{DolgHaf LLT, DS}.","short_abstract":"We prove central limit theorems, Berry-Esseen type theorems, almost sure invariance principles, large deviations and Livsic type regularity for partial sums of the form $S_n=\\sum_{j=0}^{n-1}f_j(...,X_{j-1},X_j,X_{j+1},...)$, where $(X_j)$ is an inhomogeneous Markov chain satisfying some mixing assumptions and $f_j$ is...","url_abs":"https://arxiv.org/abs/2510.07757","url_pdf":"https://arxiv.org/pdf/2510.07757v2","authors":"[\"Yeor Hafouta\"]","published":"2025-10-09T03:56:59Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.DS\",\"math.ST\"]","methods":"[]","has_code":false}