| Strong solution of Itô type set-valued stochastic differential equation |
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| 基金项目： | Supported by National Natural Science Foundation of China （Grant No. 10771010）, PHR （IHLB）, Research Fund of Beijing Educational Committee, China; and Grant-in-Aid for Scientific Research 19540140, JapanAcknowledgements We deeply thank Jinping Zhang who pointed out a crucial mistake in the previous version as well as gave us valuable comments. We also would like to thank the referees for their valuable remarks. |
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| 摘 要： | In this paper, we shall firstly illustrate why we should introduce an It5 type set-valued stochastic differential equation and why we should notice the almost everywhere problem. Secondly we shall give a clear definition of Aumann type Lebesgue integral and prove the measurability of the Lebesgue integral of set-valued stochastic processes with respect to time t. Then we shall present some new properties, especially prove an important inequality of set-valued Lebesgue integrals. Finally we shall prove the existence and the uniqueness of a strong solution to the It5 type set-valued stochastic differential equation.
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| 关 键 词： | 集值随机过程 随机微分方程 Lebesgue积分 勒贝格积分 强解 证明 不等式 |
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