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SUMMARY:Convolution tail equivalent distributions: basic properties - Prof
  Dmitri Korshunov\, (Novosibirsk)
DTSTART:20090227T140000Z
DTEND:20090227T150000Z
UID:TALK17176@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\n
 behaviour of the distribution of the random sum $S_\\tau$. We start with\n
 the description of all possible values of the limit of the ratio\n$\\overl
 ine{F \\star F}(x)/\\overline F(x)$ as $x\\to\\infty$. This problem is\ncl
 osely related to the problem of the lower limit of this ratio and goes\nba
 ck to W. Rudin. The second part of the talk is devoted to conditions\nunde
 r which $P(S_\\tau>x)\\sim E\\tau \\overline F(x)$ as $x\\to\\infty$. We\n
 also consider applications of results obtained to random walks\, compound\
 nPoisson distributions\, infinitely divisible laws\, and branching process
 es.\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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