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

Abstract : We derive a functional change of variable formula for non-anticipative functionals defined on the space of right continuous paths with left limits. The functional is only required to possess certain directional derivatives, which may be computed pathwise. Our results lead to functional extensions of the Ito 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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https://hal.archives-ouvertes.fr/hal-00471318
Contributor : Rama Cont <>
Submitted on : Tuesday, April 13, 2010 - 3:47:01 PM
Last modification on : Friday, December 18, 2020 - 6:46:05 PM
Long-term archiving on: : Thursday, September 23, 2010 - 12:11:15 PM

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Rama Cont, David-Antoine Fournie. Change of variable formulas for non-anticipative functionals on path space. Journal of Functional Analysis, Elsevier, 2010, 259 (4), pp.1043-1072. ⟨10.1016/j.jfa.2010.04.017⟩. ⟨hal-00471318v2⟩

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