Bounds for \(r\)th order joint cumulant under \(r\)th order strong mixing (Q1962241)

A new concept of \(r\)th-order strong mixing for sub \(\sigma\)-algebra of a probability space is introduced. The concept is stated by means of a convergence of a sequence of \(r\)th-order joint cumulants. A bound on an \(r\)th order joint cumulant is obtained under a two-part dependence assumption, which includes the case of \(r\)th order strong mixing. This generalizes the work of \textit{R. C. Bradley} [Stat. Probab. Lett. 30, No. 4, 287-293 (1996; Zbl 0877.62052)] and \textit{E. Rio} [Ann. Inst. Henri Poincaré, Probab. Stat. 29, No. 4, 587-597 (1993; Zbl 0798.60027)].