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CATEGORIES:Probability Theory and Statistics in High and Infi
nite Dimensions
SUMMARY:General Strassen type results for partial sum proc
esses in Euclidean space - Uwe Einmahl\, Vrije Uni
versiteit Brussel
DTSTART;TZID=Europe/London:20140625T120000
DTEND;TZID=Europe/London:20140625T123000
UID:TALK53115AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53115
DESCRIPTION:One of the classical results of probability for su
ms of i.i.d. random variables\nis the functional L
IL of Strassen (1964) who under the classical assu
mptions\nthat the second moment is nite and the e
xpectation of the underlying dis-\ntribution is eq
ual to zero showed that with probability 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 se
quence 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 ex
tends to higher dimensions and there are versions
in the innite\nvariance case where one has to use
dierent normalizing sequences fcng. In\nthe 1-di
mensional case it turned out that one still gets t
he standard cluster\nset as in the Strassen LIL pr
ovided that the normalizing sequence satises\nsom
e mild regularity assumptions. This is no longer t
he case if one looks at\nthis problem in the multi
dimensional setting.\nThe purpose of this talk is
to give a survey of some recent work in this direc
-\ntion. Among other things\, we are able to deter
mine all possible cluster sets\nin the independent
component case. In the general case we can identi
fy min-\nimal and maximal sets for the functional
cluster sets in terms of the cluster\nsets of the
normalized sums.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
CONTACT:
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