论文标题
SKOROHOD可测量的通用函数表示Semimartingale SDE的解决方案
A Skorohod measurable universal functional representation of solutions to semimartingale SDEs
论文作者
论文摘要
在本文中，我们展示了大型半明星驱动的随机微分方程的通用skorohod可测量功能表示。为此，我们证明，随机微分方程的强溶液的路径可以写入其驱动过程路径的可测量函数，进入所有Càdlàg函数的空间，该函数配备了由所有开放集生成的Borel Sigma-field，该函数与Skorohod Metric相对于所有开放式集合产生。该结果可以应用于计算由纯跳跃过程驱动的SDE的Malliavin衍生物。
In this paper we show the existence of a universal Skorohod measurable functional representation for a large class of semimartingale-driven stochastic differential equations. For this we prove that paths of the strong solutions of stochastic differential equations can be written as measurable functions of the paths of their driving processes into the space of all càdlàg functions equipped with the Borel sigma-field generated by all open sets with respect to the Skorohod metric. This result can be applied to calculate Malliavin derivatives for SDEs driven by pure-jump Lévy processes with drift.
