Change of variable formulas for non-anticipative functional on path space

Abstract : We derive a change of variable formula for non-anticipative functionals defined on the space of Rd-valued right-continuous paths with left limits. The functionals are only required to possess certain directional derivatives, which may be computed pathwise. Our results lead to functional extensions of the Itô formula for a large class of stochastic processes, including semimartingales and Dirichlet processes. In particular, we show the stability of the class of semimartingales under certain functional transformations.
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Article dans une revue
Journal of Functional Analysis, Elsevier, 2010, 259 (4), pp.1043-1072. <10.1016/j.jfa.2010.04.017>
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Contributeur : Rama Cont <>
Soumis le : samedi 16 mars 2013 - 23:45:43
Dernière modification le : jeudi 27 avril 2017 - 09:46:12

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Rama Cont, David-Antoine Fournié. Change of variable formulas for non-anticipative functional on path space. Journal of Functional Analysis, Elsevier, 2010, 259 (4), pp.1043-1072. <10.1016/j.jfa.2010.04.017>. <hal-00801537>

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