A new maximal inequality and invariance principle for stationary sequences

Abstract

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.

Published at http://dx.doi.org/10.1214/009117904000001035 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Martingale approximations for sums of stationary processes

Cited by in corpus (17)

• Strong invariance principles for dependent random variables
• Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples
• A functional limit theorem for dependent sequences with infinite variance stable limits
• On the functional central limit theorem via martingale approximation
• On martingale approximations and the quenched weak invariance principle
• Law of the iterated logarithm for stationary processes
• Comparison between criteria leading to the weak invariance principle
• Invariance principle via orthomartingale approximation
• On the normal approximation for random fields via martingale methods
• An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation
• Inference for Monotone Trends Under Dependence
• The Local to Unity Dynamic Tobit Model
• Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas
• H{ö}lderian weak invariance principle under Maxwell and Woodroofe condition
• Variance of partial sums of stationary sequences
• A small delay and correlation time limit of stochastic differential delay equations with state-dependent colored noise
• Bound on the maximal function associated to the bounded law of the iterated logarithms via orthomartingale approximation