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Comptes Rendus Mathématique
Volume 353, n° 12
pages 1153-1158 (décembre 2015)
Doi : 10.1016/j.crma.2015.09.022
Received : 10 June 2015 ;  accepted : 23 September 2015
Conditionally Gaussian stochastic integrals
Intégrales stochastiques conditionnellement gaussiennes

Nicolas Privault , Qihao She
 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore 


We derive conditional Gaussian type identities of the form
E[exp⁡(i∫0TutdBt)|∫0T|ut|2dt]=exp⁡(−12∫0T|ut|2dt), for Brownian stochastic integrals, under conditions on the process   specified using the Malliavin calculus. This applies in particular to the quadratic Brownian integral   under the matrix condition  , using a characterization of Yor [[6]].

The full text of this article is available in PDF format.

Nous obtenons des identités gaussiennes conditionnelles de la forme
E[exp⁡(i∫0TutdBt)|∫0T|ut|2dt]=exp⁡(−12∫0T|ut|2dt), pour les intégrales stochastiques browniennes, sous des conditions sur le processus   exprimées à l'aide du calcul de Malliavin. Ces résultats s'appliquent en particulier à l'intégrale brownienne quadratique   sous la condition matricielle  , en utilisant une caractérisation de Yor [[6]].

The full text of this article is available in PDF format.

Keywords : Quadratic Brownian functionals, Multidimensional Brownian motion, Moment identities, Characteristic functions

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