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SUMMARY:Convolution tail equivalent distributions: basic properties (Joint
  with Networks (OR) seminar). - Dmitri Korshunov (Novosibirsk)
DTSTART:20090227T140000Z
DTEND:20090227T150000Z
UID:TALK17206@talks.cam.ac.uk
CONTACT:Neil Walton
DESCRIPTION:The talk discusses the tail behaviour of 2-fold convolutions $
 \\overline{F \\star F}$ of right-unbounded distributions and to the tail b
 ehaviour of the distribution of the random sum $S_\\tau$. We start with th
 e description of all possible values of the limit of the ratio $\\overline
 {F \\star F}(x)/\\overline F(x)$ as $x\\to\\infty$. This problem is closel
 y related to the problem of the lower limit of this ratio and goes back to
  W. Rudin. The second part of the talk is devoted to conditions under whic
 h $P(S_\\tau>x)\\sim E\\tau \\overline F(x)$ as $x\\to\\infty$. We also co
 nsider applications of results obtained to random walks\, compound Poisson
  distributions\, infinitely divisible laws\, and branching processes.\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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