The asymptotic behaviour of maxima of complete and incomplete samples from stationary sequences

Abstract

Let {Xn,n>=1} be a strictly stationary sequence of random variables and Mn=max{X1,X2,...,Xn}. Assume that some random variables X1,X2,... can be observed and the sequence of random variables indicate which X1,X2,... are observed, thus . In paper (Mladenovic and Piterbarg, 2006 [3]), the limiting behaviour is investigated under the condition for some real p[set membership, variant](0,1). We generalize these results on the case, when for some random variable [lambda]Stationary sequences Weak dependency