文章基本信息

标题：Geometry of Stochastic Delay Differential Equations
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作者：Catuogno, Pedro José ; Ruffino, Paulo R. C.
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2005
卷号：10
页码：190-195
DOI：10.1214/ECP.v10-1151
出版社：Electronic Communications in Probability
摘要：Stochastic delay differential equations (SDDE) on a manifold $M$ depend intrinsically on a connection $\nabla$ in this space. The main geometric result in this notes concerns the horizontal lift of solutions of SDDE on a manifold $M$ to an SDDE in the frame bundle $BM$, hence the lifted equation should come together with the prolonged horizontal connection $\nabla^H$ on $BM$. We show that every horizontal semimartingale can be represented as a solution of an SDDE.