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2005 Geometry of Stochastic Delay Differential Equations
Pedro Catuogno, Paulo Ruffino
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Electron. Commun. Probab. 10: 190-195 (2005). DOI: 10.1214/ECP.v10-1151


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.


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Pedro Catuogno. Paulo Ruffino. "Geometry of Stochastic Delay Differential Equations." Electron. Commun. Probab. 10 190 - 195, 2005.


Accepted: 7 September 2005; Published: 2005
First available in Project Euclid: 4 June 2016

zbMATH: 1111.60041
MathSciNet: MR2162818
Digital Object Identifier: 10.1214/ECP.v10-1151

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