半鞅边缘分布的模拟
Mimicking the marginal distributions of a semimartingale
摘要：
我们展示的条件下，一个不连续的半鞅$ξ$的边缘分布流可以匹配的马尔可夫过程，其无穷小生成元表示的局部特征的$ξ$。我们的结构适用于一个大类的半鞅，包括马尔可夫过程的光滑函数。我们利用这个结果导出了半鞅一维分布的偏积分微分方程，将Kolmogorov向前方程推广到非马尔可夫情形。
英文摘要：
We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $ξ$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $ξ$. Our construction applies to a large class of semimartingales, including smooth functions of a Markov process. We use this result to derive a partial integro-differential equation for the one-dimensional distributions of a semimartingale, extending the Kolmogorov forward equation to a non-Markovian setting.
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