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  3. Lévy Processes in Lie Groups
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2009
      May 2004
      ISBN:
      9780511546624
      9780521836531
      DOI:
      https://doi.org/10.1017/CBO9780511546624
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.53kg, 276 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
      Series:
      Cambridge Tracts in Mathematics (162)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
    Series:
    Cambridge Tracts in Mathematics (162)
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    Book description

    The theory of Lévy processes in Lie groups is not merely an extension of the theory of Lévy processes in Euclidean spaces. Because of the unique structures possessed by non-commutative Lie groups, these processes exhibit certain interesting limiting properties which are not present for their counterparts in Euclidean spaces. These properties reveal a deep connection between the behaviour of the stochastic processes and the underlying algebraic and geometric structures of the Lie groups themselves. The purpose of this work is to provide an introduction to Lévy processes in general Lie groups, the limiting properties of Lévy processes in semi-simple Lie groups of non-compact type and the dynamical behavior of such processes as stochastic flows on certain homogeneous spaces. The reader is assumed to be familiar with Lie groups and stochastic analysis, but no prior knowledge of semi-simple Lie groups is required.

    Reviews

    '… an outstanding addendum to the literature on modern probability theory.'

    Source: Mathematical Reviews

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