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

  title={Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples},
  author={Florence Merlev{\`e}de and Magda Peligrad},
The aim of this paper is to propose new Rosenthal-type inequalities for moments of order p larger 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. (2007) and Rio (2009), 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’s maximal inequality for… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 49 references

Moment inequalities for sums of dependent random variables under projective conditions

E. Rio
J. Theoret. Probab • 2009
View 14 Excerpts
Highly Influenced

An empirical central limit theorem for dependent sequences

J. Dedecker, C Prieur
Stochastic Process • 2007
View 6 Excerpts
Highly Influenced

Introduction to strong mixing conditions. Volumes 1-3

R. C. Bradley
View 4 Excerpts
Highly Influenced

Inequalities for absolutely regular sequences: application to density estimation

G. Viennet
Probab. Theory Related Fields • 1997
View 5 Excerpts
Highly Influenced

Comparison of martingale difference sequences

J. Zinn
In Probability in Banach spaces, V, Lecture Notes in Math. 1153, • 1985
View 4 Excerpts
Highly Influenced

Martingale Limit Theory and its Applications

P. Hall, C. C. Heyde
View 9 Excerpts
Highly Influenced

Convergence of Probability Measures

P. Billingsley
View 8 Excerpts
Highly Influenced

Rates of convergence in the central limit theorem for linear statistics of martingale differences

J. Dedecker, F. Merlevède
Stochastic Process • 2011
View 7 Excerpts
Highly Influenced

Similar Papers

Loading similar papers…