Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Oleksandr Zadorozhnyi (Uni Potsdam)
In this talk I firstly discuss a general martingale-difference approach which can be used to obtain some of the existing concentration inequalities for 1-dimensional weakly-dependent random processes. In this framework a martingale-difference approach and a (martingale-like) dependence conditions can be generalised to the case of high dimension. Using one of such weak-dependency conditions of projective kind I present the variants of Azuma-Hoeffding’s and Burkholder’s inequalities for random fields indexed with d-dimensional rectangles and compare it to the existing results in the field.
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