Modeling and approximation of stochastic differential equations driven by semimartingales
Modeling and approximation of stochastic differential equations driven by semimartingales
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DOI：
10.1080/17442508108833165
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发表时间：
1981
期刊：
影响因子：
--
通讯作者：
S. Marcus
中科院分区：
文献类型：
--
作者：
S. Marcus
研究了具有跳跃分量和连续分量的半鞅驱动的随机微分方程的建模和逼近问题。利用半鞅理论，定义并分析了Mcshane正则扩展和Fisk-Stratonovich随机微分方程的推广模型。证明了这种广义正则扩展具有许多与Mcshane扩展相同的理想性质，但它适用于更广泛的一类噪声过程。特别地，证明了几个近似（或连续性或稳定性）结果；这些表明（在不同的假设集和不同的拓扑结构下），如果噪声过程序列zm收敛于噪声过程z，那么对应于zm的正则扩展的解收敛于对应于z的解。
The modeling and approximation of stochastic differential equations driven by semi-martingales with both jump and continuous components are considered. A model, which is a generalization of Mcshane's canonical extension and the stochastic differential equations of Fisk-Stratonovich, is defined and analyzed by means of the theory of semimartingales. It is proved that this generalized canonical extension possesses many of the same desirable properties as that of Mcshane, but it is applicable to a much wider class of noise processes. In particular, several approximation (or continuity or stability) results are proved; these show (under various sets of hypotheses and in various topologies) that if a sequence of noise processes z m converges to a noise process z, then the solutions of the canonical extension corresponding to z m converge to the solution corresponding to z.