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Geometry of Stochastic Delay Differential Equations

   
@article{ECP1151,
	author = {Pedro Catuogno and Paulo Ruffino},
	title = {Geometry of Stochastic Delay  Differential Equations},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {10},
	year = {2005},
	keywords = {},
	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.},
	pages = {no. 19, 190-195},
	issn = {1083-589X},
	doi = {10.1214/ECP.v10-1151},    
        url = {http://ecp.ejpecp.org/article/view/1151}}