Abstract.
Let $(X_n)$ be a strictly stationary random sequence with the marginal distribution functions $F(x)=P{X_1\leq x}$. Suppose that some of random variables $X_1, X_2, X_3...$ can be observed, and let $\varepsilon_k$ be the indicator of the event that random variables $X_k$ is observed and $S_n=\varepsilon_1+...+\varepsilon_n$. Let us denote $ M_n=\max {X_1,...,X_n } $, \tilde{M_n}= \max {X_j : 1\leq j \leq n, \varepsilon_j=1 }. Suppose that $F$ belongs to the maximum domain of attraction of some of extreme value distributions. The limiting distributions of the random vector $(\tilde{M_n}, M_n)$ and "asymptotic independency" of $\tilde{M_n}$ and $M_n$ are obtained under some condition of weak dependency of random variables from sequence $(X_n)$, which is more restrictive than Leadbetter's $D(u_n)$ condition, and some conditions on the sequence $(\varepsilon_n)$. Some results concerning estimation of the exponent of regular variation using a sample with the missing observations will also be presented.

Координаторами Большого кафедрального семинара на осенний семестр 2004 года назначены профессор Тюрин Юрий Николаевич и доцент Болдин Михаил Васильевич.