Sums whose terms are elements of linear random regression sequences. Asymptotic properties

      Аннотация: One-dimensional and multi-dimensional linear regression sequences, sequences of partial sums, and series whose terms are elements of regression sequences appear as mathematical models in different fields of modern science. Their various applications in physics, economics, biology, cybernetics, actuary and financial mathematics motivate further study of the topic. In this book, we study the asymptotic behaviour of sequences of sums whose terms are elements of one-dimensional and multi-dimensional linear regressions with independent and symmetric noise. In particular, a great attention is paid to conditions which provide the almost sure convergence of series with regression terms. These problems are considered in both finite-dimensional and separable Banach spaces. This book is a result of joint successful work by Dr. Prof. V. Buldygin and Dr. M. Runovska.

Ключевые слова: linear regressive sequences, asymptotic behaviour of sums of elements of random sequences, convergence almost surely of random series, Gaussian Markov sequences, Gaussian m-Markov sequences, m-th order regressive sequences, operator-normed sums of independent random vectors