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UID:20250712T130258EDT-9820VoWCU7@132.216.98.100
DTSTAMP:20250712T170258Z
DESCRIPTION:Title: Stochastic calculus for the theta process.\n\nAbstract: 
 The theta process is a stochastic process of number theoretical origin ari
 sing from a scaling limit of quadratic Weyl exponential sums. It shares ma
 ny properties in common with the Brownian motion such as its Hölder contin
 uity\, covariance structure\, quadratic variation\, scaling properties and
  so on but crucially we show it is not a semimartingale. The theta process
  can be described as a map on a particular 6 dimensional Lie group along w
 ith an automorphic function. As the theta process is not a semimartingale\
 , Itô techniques are not applicable. However\, a more modern theory of sto
 chastic calculus known as rough paths theory is applicable. In this talk w
 e discuss the construction a rough path above the theta process. The rough
  path (iterated integrals) of the theta process are constructed using homo
 genous dynamics and representation theory\, and again can be described in 
 terms of a Lie group and a higher rank automorphic function.\n\n \n
DTSTART:20250116T163000Z
DTEND:20250116T173000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Zachary Selk (Queen’s University)
URL:/mathstat/channels/event/zachary-selk-queens-unive
 rsity-362479
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