Maximal inequalities for \(N\)-demimartingale and strong law of large numbers
Let \(\{S_n,\, n\geq 1\}\) be an \(L^1\) sequence of random variables and suppose that \[ E[(S_{j+1}-S_j)f(S_1,\dots,S_j)] \leq 0 \] for all coordinatewise nondecreasing functions \(f\) for which the expectation is defined. Such a sequences \(\{S_n,\, n \geq 1\}\) is called a \(N\)-demimartingale [\textit{T. C. Christofides}, Arch. Inequal. Appl. 1, No. 3--4, 387--397 (2003; Zbl 1051.60021); \textit{B. L. S. Prakasa Rao}, J. Indian Soc. Agric. Stat. 57, Spec. Issue, Article No. 21, 208--216 (2004; Zbl 1188.60020)]. The authors derive some maximal inequalities for \(N\)-demimartingales. As applications of these inequalities, they prove a strong law of large numbers and obtain some related results.
scientific article; zbMATH DE number 5932100