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SUMMARY:Martingale calculus and a maximal inequality for supermartingales 
 - Hajek\, B (Illinois)
DTSTART:20100315T150000Z
DTEND:20100315T170000Z
UID:TALK23794@talks.cam.ac.uk
CONTACT:Neil Walton
DESCRIPTION:In the first hour of this two-part presentation\, the calculus
  of semimartingales\, which includes martingales with both continuous and 
 discrete compotents\, will be reviewed. In the second hour of the presenta
 tion\, a tight upper bound is given involving the maximum of a supermartin
 gale. Specifically\, it is shown that if Y is a semimartingale with initia
 l value zero and quadratic variation process [Y\, Y] such that Y + [Y\, Y]
  is a supermartingale\, then the probability the maximum of Y is greater t
 han or equal to a positive constant is less than or equal to 1/(1+a). The 
 proof uses the semimartingale calculus and is inspired by dynamic programm
 ing. If Y has stationery independent increments\, the bounds of JFC Kingma
 n apply to this situation. Complements and extensions will also be given.\
 n
LOCATION:MR4\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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