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Probabilities on vector spaces

  • Wilfried Hazod
  • Eberhard Siebert
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 531)

Abstract

The first chapter focusses on limit laws of operator-normalized sums of i.i.d. sequences of vector-space-valued random variables; the theory is developed to an extent which has a counterpart in the theory of group-valued random variables. Thus, in particular, the investigations concentrate on only finite-dimensional (hence locally compact) vector spaces. Therefore we are concerned with a particular case of the ‘classical’ theory of infinitely divisible laws on ℝ d . It is assumed that the reader is familiar with the classical Lévy—Khinchin formula. However, we are aware that the main themes, like operator- (semi-) stability and domains of attraction, do not belong to the standard repertoire of students and researchers in probability, and so we develop this branch of the theory ab ovo.

Keywords

Closed Subgroup Maximal Compact Subgroup Convolution Semigroup Decomposability Group Large Symmetry Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Wilfried Hazod
    • 1
  • Eberhard Siebert
  1. 1.Mathematical DepartmentUniversity of DortmundDortmundGermany

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