Akbash K. Asymptotic behavior of extreme values of random vectors

The dissertation is devoted to investigation of asymptotic behavior of extreme values of random vectors in infinite-dimensional spaces. The Marcinkiewicz-Zygmund order law of large numbers is set for random variables in Banach lattices. Similar results are also obtained for the maximum scheme. The next important step - the order law of large numbers is set for random variables in -convex Banach lattices where the normalized set is ( is monotonically-increasing continuous function). Ordinal law of large numbers is set for random elements in -convex Banach lattices. There are well-known for results of maximum asymptotic stability of independent random variables on -concave Banach ideal spaces that are being generalized at work. And also one theorem of maximum relative asymptotic stability is being obtained. The low bound is found in the law of the iterated logarithm for maximum scheme in . Important exponential estimates in the law of the iterated logarithm for extreme values of a sequence of independent random variables are obtained. Laws of the iterated logarithm for extreme values of a sequence of general random elements in some Banach lattices are obtained.