## Electronic Communications in Probability

### Geometry of Stochastic Delay Differential Equations

#### Abstract

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.

#### Article information

Source
Electron. Commun. Probab., Volume 10 (2005), paper no. 19, 190-195.

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

https://projecteuclid.org/euclid.ecp/1465058084

Digital Object Identifier
doi:10.1214/ECP.v10-1151

Mathematical Reviews number (MathSciNet)
MR2162818

Zentralblatt MATH identifier
1111.60041

Rights

#### Citation

Catuogno, Pedro; Ruffino, Paulo. Geometry of Stochastic Delay Differential Equations. Electron. Commun. Probab. 10 (2005), paper no. 19, 190--195. doi:10.1214/ECP.v10-1151. https://projecteuclid.org/euclid.ecp/1465058084

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