Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables
By Sergey Utev, Magda Peligrad. 2003
143 citations recorded by the source corpus.
Subfields: Finance, Management Science and Operations Research, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f1d9a8407bf2fe88395096d55f393840e9e577e8
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Citations in the corpus
- On asymptotic approximation of inverse moments for a class of nonnegative random variables (2014, background): “See for example, φ mixing identically distributed random variables with ∑∞ n= φ1/2(2n) < ∞ (see [19]), ρ mixing identically distributed random variables with ∑∞ n= ρ2/p(2n) < ∞ (see [20]), negatively associated random variables (see [21]), ρ̃ mixing random variables (see [22]), negatively dependent ”
- Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples (2011, methodology): “…for the case of ρ-mixing sequences; Shao (1988), Peligrad (1989) and Utev (1991) for the case of φ-mixing sequences; Peligrad and Gut (1999) and Utev and Peligrad (2003) for interlaced mixing; Theorem 2.2 in Viennet (1997) for β-mixing processes; Theorem 6.3 in Rio (2000) for the strongly…”
- Recent advances in invariance principles for stationary sequences (2006, background): “ where this supremum is taken over all pairs of nonempty finite sets S,T of Z such that dist(S,T) ≥ n. The following inequality follows. See Peligrad [50, 51], Peligrad and Gut [53], Utev and Peligrad [66] for details. Theorem 10 For a positive integer N ≥ 1 and positive real numbers q ≥ 2 and 0 ≤ r ”
- Probability and moment inequalities under dependence (2013, methodology): “Under various types of strong mixing conditions, the Rosenthal type inequalities have been obtained for dependent random variables; see Shao (1988, 1995, 2000), Peligrad (1985, 1989), Utev and Peligrad (2003), and Rio (2000).”