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Brownian sheet and time inversion -- From $G$-orbit to $L(G)$-orbit

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 نشر من قبل Manon Defosseux
 تاريخ النشر 2021
  مجال البحث
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 تأليف Manon Defosseux




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We have proved in a previous paper that a space-time Brownian motion conditioned to remain in a Weyl chamber associated to an affine Kac-Moody Lie algebra is distributed as the radial part process of a Brownian sheet on the compact real form of the underlying finite dimensional Lie algebra, the radial part being defined considering the coadjoint action of a loop group on the dual of a centrally extended loop algebra. We present here a very brief proof of this result based on a time inversion argument and on elementary stochastic differential calculus.



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