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Pitman transforms and Brownian motion in the interval viewed as an affine alcove

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 نشر من قبل Manon Defosseux
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English
 تأليف Philippe Bougerol




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Pitmans theorem states that if {Bt, t $ge$ 0} is a one-dimensional Brownian motion, then {Bt -- 2 inf s$le$t Bs, t $ge$ 0} is a three dimensional Bessel process, i.e. a Brownian motion conditioned in Doob sense to remain forever positive. In this paper one gives a similar representation for the Brownian motion in an interval. Due to the double barrier, it is much more involved and only asymptotic. This uses the fact that the interval is an alcove of the Affine Lie algebra A 1 1 .



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