Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples

By F. Merlevède, Magda Peligrad. 2011

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The aim of this paper is to propose new Rosenthal-type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by Peligrad et al. [Proc. Amer. Math. Soc. 135 (2007) 541–550] and Rio [J. Theoret. Probab. 22 (2009) 146–163], the estimates of the moments are expressed in terms of the norms of projections of partial sums. The proofs of the results are essentially based on a new maximal inequality generalizing the Doob maximal inequality for martingales and dyadic induction. Various applications are also provided.

Subfields: Mathematical Physics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/af49b3285b1c3b1acd6a085711b4c7e24e9f64ae

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In Mathematical Physics

In Numerical Analysis

In Statistics and Probability

Citations in the corpus

Probability and moment inequalities under dependence (2013, background): “…+∆1/2N +DN ), (2.1) where N = min{i : 2i ≥ n} and σN = ∥X0∥2 + 1 2 N−1∑ l=0 2−l/2∥E(S2l |F0)∥2, ∆N = N−1∑ l=0 2−2l/p∥E(S22l |F0)− E(S 2 2l)∥p/2, DN = N−1∑ l=0 2−l/p∥E(S2l |F0)∥p. Merlevède and Peligrad (2011) obtained the following: for all p > 2, ∥S∗n∥p ≤ cpn1/p [ ∥X0∥p+ n∑ k=1 ∥E(Sk|F0)∥p…”