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UID:5953@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220927T143000
DTEND;TZID=Europe/Paris:20220927T150000
DTSTAMP:20241120T200704Z
URL:https://www.i2m.univ-amu.fr/evenements/some-observations-on-convex-hul
 ls-of-stable-random-walks/
SUMMARY:Stjepan Sebek (University of Zagreb\, Croatia): Some observations o
 n convex hulls of stable random walks
DESCRIPTION:Stjepan Sebek: We consider convex hulls of random walks whose s
 teps belong to the domain of attraction of a stable law in R^d. We prove c
 onvergence of the convex hull in the space of all convex and compact subse
 ts of R^d\, equipped with the Hausdorff distance\, towards the convex hull
  spanned by a path of the limit stable Lévy process. As an application\, 
 we establish convergence of (expected) intrinsic volumes under some mild m
 oment/structure assumptions posed on the random walk. Using the obtained r
 esult in the case when the limiting object is a Brownian motion\, we devel
 op a closed formula for the expected value of the d-dimensional volume of 
 the convex hull spanned by the time-space trajectory of the (d−1)-dimens
 ional Brownian motion run up to time one.\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 022/09/Stjepan_Sebek.png
CATEGORIES:Séminaire,Probabilités
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