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UID:20260620T193016EDT-44453Nx1uV@132.216.98.100
DTSTAMP:20260620T233016Z
DESCRIPTION:Title: Stable Lévy motion with values in the Skorohod space: co
 nstruction and approximation\n\nAbstract: Regularly varying random variabl
 es play an important role in probability theory\, being used as models for
  heavy-tailed observations (observations which may assume extreme values w
 ith high probability). With the rapid advancement of technology\, data is 
 no longer observed at fixed moments of time\, but continuously over a fixe
 d interval in time or space (which we may identify with the interval [0\,1
 ]). If this measurement is expected to exhibit a sudden drop or increase o
 ver this fixed interval\, then an appropriate model for it could be a rand
 om element in an infinite dimensional space\, such as the Skorohod space D
 =D([0\,1]) of cadlag functions on [0\,1] (i.e. right-continuous functions 
 with left limits). In this talk\, we examine the macroscopic limit (as tim
 e gets large) of the partial sum sequences associated to i.i.d. regularly 
 varying elements with values in $D$. This limit is an interesting object i
 n itself\, which we call a 'D-valued stable Levy motion''.Our methods were
  inspired by the construction of the classical stable Levy motion (in dime
 nsion $d$)\, and of its approximation by partial sums of i.i.d. regularly 
 varying vectors. Our goal is to extend these results to the infinite-dimen
 sional setting\, using the concept of regular variation for random element
 s in D introduced by de Haan and Lin (2001)\, and developed further by Hul
 t and Lindskog (2005).\n	This talk is based on joint work with doctoral stu
 dent Becem Saidani.\n
DTSTART:20190218T190000Z
DTEND:20190218T190000Z
LOCATION:Room 1205\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Raluca Balan (University of Ottawa)
URL:/mathstat/channels/event/raluca-balan-university-o
 ttawa-294720
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