| 引用本文: | 屈田兴,金治明.关于半鞅向量随机积分的两个结果.[J].国防科技大学学报,2008,30(2):135-138.[点击复制] |
| QU Tianxing,JIN Zhiming.Two Results about the Vector Stochastic Integrals with Respect to Semimartingales[J].Journal of National University of Defense Technology,2008,30(2):135-138[点击复制] |
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| 关于半鞅向量随机积分的两个结果 |
| 屈田兴, 金治明 |
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(国防科技大学 理学院，湖南 长沙 410073)
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| 摘要: |
| 首先利用半鞅Girsanov定理与闭图像定理证明了：若｛Xn｝是带滤基的完备概率空间(Ω，F，F，P)中的一列半鞅，其中滤基F=(Ft)t≥0满足通常条件，且｛Xn｝在关于P的Emery拓扑空间中收敛于X，则当概率测度Qloc《P时，｛Xn｝在关于Q的Emery拓扑空间中也收敛于X。在此基础上又证明了：若X是关于P的d维半鞅，d维可料过程H关于P在半鞅向量随机积分的意义下对X可积，则当概率测度Qloc《P时，H关于Q在半鞅向量随机积分的意义下也对X可积，并且两种积分是Q-无区别的。由于Q《P强于Qloc《P，故本文推广了文献［1］中的引理4.9与定理4.14。 |
| 关键词: 半鞅 向量随机积分 概率测度的局部连续性 可料过程 |
| DOI： |
| 投稿日期：2008-01-22 |
| 基金项目:国家自然科学基金资助项目(60673090) |
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| Two Results about the Vector Stochastic Integrals with Respect to Semimartingales |
| QU Tianxing, JIN Zhiming |
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(College of Science, National Univ. of Defense Technology，Changsha 410073, China)
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| Abstract: |
| Let｛Xn｝ be a sequence of semimartingale in a filtered complete probability space (Ω，F，F，P) satisfying the usual condition. We use the general Girsanov thorem and closed graph theorem to prove that the sequence ｛Xn｝converges on X in the Emery topology w.r.t Q if｛Xn｝ converges on X in the Emery topology w.r.t P and the probability measureQloc《P. In light of this fact, we prove that if X is a d-dimensional semimartingale and a d-dimensional predictable process，H is X-integrable in the sense of vector stochastic integrals w.r.t P， when the probability measure Qloc《P, H is also X-integrable in the sense of vector stochastic integrals w.r.t Qand these two integrals are Q-differentiable. It is noted that the condition of Q《P is stronger than that of Qloc《P, therefore, this paper generalizes lemma 4.9 and theorem 4.14 in［1］. |
| Keywords: semimartingale vector stochastic integral locally absolutely continuity of probability measure predictable process |
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