Randomized multivariate Central Limit Theorems for ergodic homogeneous random fields

Arkady Tempelman

Stochastic Processes and their Applications, 2022, vol. 143, issue C, 89-105

Abstract: We present new versions of the CLT which are valid for each ergodic homogeneous multivariate random field (X1(⋅),…,Xd(⋅)) on Rm or Zm(m≥1) (in particular, for each ergodic stationary random process and for each ergodic stationary random sequence) such that for all l E[|Xl(0)|2+δ]<∞ for some δ>0(l=1,...,d); in some statements ergodicity is not assumed. Randomization made it possible to significantly weaken the strong mixing conditions and other restrictions of dependence, that are imposed in the conventional CLTs. These results pave the way to consistent statistical inference for homogeneous random fields and stationary processes with strong dependence.

Keywords: Central Limit Theorem; Pointwise Ergodic Theorem; Stationary random process; Homogeneous random field (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:143:y:2022:i:c:p:89-105

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DOI: 10.1016/j.spa.2021.10.006

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