Stochastic Differential Equations Driven by Spatial Parameters Semimartingale with Non-Lipschitz Local Characteristic |
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| Authors: | Zongxia Liang |
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| Affiliation: | (1) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China |
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| Abstract: | We study m-dimensional SDE  , where  ,  , is a continuous  -valued (spatial) semimartingale with local characteristic ( a,b)(cf. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, UK, 1990). We establish non-explosion, existence and pathwise uniqueness theorems and non-contact property of strong solutions to the SDE for which the local characteristic (a,b) satisfies non-Lipschitz conditions. This work is supported by NSFC. |
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| Keywords: | non-Lipschitzian non-contact property non-explosion pathwise uniqueness local characteristic |
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