Change of variable formulas for non-anticipative functionals on path space ✩
Change of variable formulas for non-anticipative functionals on path space ✩
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DOI：
10.1016/j.jfa.2010.04.017
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发表时间：
2010-04
影响因子：
1.7
通讯作者：
R. Cont;David-Antoine Fournié
中科院分区：
文献类型：
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作者：
R. Cont;David-Antoine Fournié
给出了定义在具有左极限的Rd-值右连续路空间上的非预期泛函的变量变换公式。泛函只需要具有某些方向导数，这些方向导数可以按路径计算。我们的结果导致功能扩展的伊藤公式的一大类随机过程，包括半鞅和Dirichlet过程。特别地，我们证明了半鞅类在某些函数变换下的稳定性。
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.