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Asymptotic distribution (Probability theory) --- Asymptotic expansions --- Asymptotic expansions. --- Asymptotic distribution (Probability theory).

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This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.

Random walks (Mathematics) --- Asymptotic distribution (Probability theory) --- Asymptotic expansions.

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This book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas.

Differential equations --- Asymptotic distribution (Probability theory) --- Asymptotic expansions --- Central limit theorem --- Distribution (Probability theory) --- 517.91 Differential equations --- Asymptotic theory.

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Mathematical statistics --- Asymptotic distribution (Probability theory) --- Estimation theory --- Statistical functionals --- 519.21 --- Probability theory. Stochastic processes --- 519.21 Probability theory. Stochastic processes

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Approximation theory. --- Probabilities. --- Théorie de l'approximation --- Probabilités --- Central limit theorem. --- Convergence. --- Functions --- Asymptotic distribution (Probability theory) --- Limit theorems (Probability theory)