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SUMMARY:General Strassen type results for partial sum processes in Euclide
 an space - Uwe Einmahl\, Vrije Universiteit Brussel
DTSTART:20140625T110000Z
DTEND:20140625T113000Z
UID:TALK53115@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:One of the classical results of probability for sums of i.i.d.
  random variables\nis the functional LIL of Strassen (1964) who under the 
 classical assumptions\nthat the second moment is nite and the expectation
  of the underlying dis-\ntribution is equal to zero showed that with proba
 bility one\, the sequence\nfS(n)=\np\n2n log log ng where S(n) : \n ! C[0\
 ; 1] is the partial sum process of\norder n\; is relatively compact in C[0
 \; 1] and moreover that the (random) set\nof limit points of this sequence
  is equal to a certain deterministic subset of\nC[0\; 1] which we call the
  cluster set of the sequence fS(n)=\np\n2n log log ng.\nThis result extend
 s to higher dimensions and there are versions in the innite\nvariance cas
 e where one has to use dierent normalizing sequences fcng. In\nthe 1-dime
 nsional case it turned out that one still gets the standard cluster\nset a
 s in the Strassen LIL provided that the normalizing sequence satises\nsom
 e mild regularity assumptions. This is no longer the case if one looks at\
 nthis problem in the multidimensional setting.\nThe purpose of this talk i
 s to give a survey of some recent work in this direc-\ntion. Among other t
 hings\, we are able to determine all possible cluster sets\nin the indepen
 dent component case. In the general case we can identify min-\nimal and ma
 ximal sets for the functional cluster sets in terms of the cluster\nsets o
 f the normalized sums.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
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