Since the pioneering works of C.C. Heyde, A.V. Nagaev, and S.V. Nagaev in 1960’s and 1970’s, the precise asymptotic behavior of large-deviation probabilities of sums of heavy-tailed random variables has been extensively investigated by many people, but mostly it is assumed that the random variables under discussion are independent. In this paper, we extend the study to the case of negatively de...

A general parameter process defined by a continuum of random variables is not jointly measurable with respect to the usual product σ-algebra. For the case of independent random variables, a one-way Fubini extension of the product space was constructed in [11] to satisfy a limited form of joint measurability. For the general case we show that this extension exists if and only if there is a count...

The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...