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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Journal articles
Journal of Functional Analysis, Elsevier, 2010, 259 (4), pp.1043-1072. <10.1016/j.jfa.2010.04.017>
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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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