We prove the existence of quasi-left continuous semimartingales with continuous local semimartingale characteristics which satisfy a Lyapunov-type or a linear growth condition, where latter takes the whole history of the paths into consideration. The proof is based on an approximation and a tightness argument and the martingale problem method.

中文翻译：

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具有连续特征的半mart的存在

我们证明了具有满足Lyapunov型或线性增长条件的连续局部半mart特征的准左连续半mart的存在，后者考虑了路径的整个历史。证明基于近似和紧密度参数以及and问题方法。