A new maximal inequality and invariance principle for stationary sequences

By Magda Peligrad, Sergey Utev. 2004

127 citations recorded by the source corpus.

We derive a new maximal inequality for stationary sequences under a martingale-type condition introduced by Maxwell and Woodroofe [Ann. Probab. 28 (2000) 713-724]. Then, we apply it to establish the Donsker invariance principle for this class of stationary sequences. A Markov chain example is given in order to show the optimality of the conditions imposed.

Subfields: Finance, Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/676a5f52a6fba16b894e56f476702e6ffda414d7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Management Information Systems

In Management Science and Operations Research

Citations in the corpus

Law of the iterated logarithm for stationary processes (2006, background): “It can also be shown that (2) is best possible through Peligrad and Utev [13].”
On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria (2007, background): “In the same context, Peligrad and Utev [20] have proved that the WIP holds under the normalization sn =√n provided that ∑”
Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples (2011, methodology): “The proof is completed by the arguments developed in the proof of Lemma 11 and by using Lemma 38 by taking into account the inequalities (24) and (25) .”
A functional limit theorem for dependent sequences with infinite variance stable limits (2010, background): “, Billingsley [7], Herrndorf [23], Merlevède and Peligrad [34], and Peligrad and Utev [37]).”
Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions (2009, methodology): “Remark 4.1 Applying (a) with δ = 1/2 and p ≥ 2 we get that Sn(f ) satisfies the Marcinkiewicz-Zygmund inequality of [ 12 ] for any f in L p (π) verifying (4.2)”
Recent advances in invariance principles for stationary sequences (2006, methodology): “the convergence of the stochastic processes n−1/2Wn(t) to the Brownian motion) and at the same time to avoid the requirement of ergodicity, Peligrad and Utev [55] followed a different approach that is described in what follows.”
WEAKLY DEPENDENT CHAINS WITH INFINITE MEMORY (2007, result): “Note also that approximations by martingale difference as in [28] or projective criterion as in [27] give the CLT under weaker assumptions for some of the examples treated in section 4.”
Asymptotic theory for stationary processes (2011, background): “For central limit theorems for stationary processes see Ibragimov (1962), Gordin (1969), Ibragimov and Linnik (1971), Gordin and Lifsic (1978), Peligrad (1996), Doukhan (1999), Maxwell and Woodroofe (2000), Rio (2000), Peligrad and Utev (2005), Dedecker et al (2007) and Bradley (2007).”