Moderate deviations and local limit theorems for the coefficients of random walks on the general linear group

Hui Xiao, Ion Grama and Quansheng Liu

Stochastic Processes and their Applications, 2023, vol. 158, issue C, 103-133

Abstract: Consider the random walk Gn:=gn…g1, n⩾1, where (gn)n⩾1 is a sequence of independent and identically distributed random elements with law μ on the general linear group GL(V) with V=Rd. Under suitable conditions on μ, we establish Cramér type moderate deviation expansions and local limit theorems with moderate deviations for the coefficients 〈f,Gnv〉, where v∈V and f∈V∗. Our approach is based on the Hölder regularity of the invariant measure of the Markov chain Gn⋅x=RGnv on the projective space of V with the starting point x=Rv, under the changed measure.

Keywords: Random walks on groups; Coefficients; Cramér type moderate deviations; Local limit theorem (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:158:y:2023:i:c:p:103-133

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DOI: 10.1016/j.spa.2022.12.013

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