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  3. Asymptotic Analysis of Random Walks
  • Cited by 29
      • A. A. Borovkov, Sobolev Institute of Mathematics, Russia
      • Translated by V. V. Ulyanov, Lomonosov Moscow State University and National Research University Higher School of Economics, Moscow, Mikhail Zhitlukhin, Steklov Institute of Mathematics, Moscow
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    • Publisher:
      Cambridge University Press
      Publication date:
      16 October 2020
      29 October 2020
      ISBN:
      9781139871303
      9781107074682
      DOI:
      https://doi.org/10.1017/9781139871303
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.84kg, 436 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Probability Theory and Stochastic Processes, Mathematical Modeling and Methods, Statistics and Probability
      Series:
      Encyclopedia of Mathematics and its Applications (176)
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    Subjects:
    Mathematics (general), Mathematics, Probability Theory and Stochastic Processes, Mathematical Modeling and Methods, Statistics and Probability
    Series:
    Encyclopedia of Mathematics and its Applications (176)
    Information

    Book description

    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.

    Reviews

    ‘… an important acquisition for a library supporting a large research group in random walks.’

    M. Bona Source: Choice

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