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 Electronic Communications in Probability > Vol. 10 (2005) > Paper 19 open journal systems 


Geometry of Stochastic Delay Differential Equations

Pedro José Catuogno, Universidade Estadual de Campinas, Brazil
Paulo R. C. Ruffino, Universidade Estadual de Campinas, Brazil


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.


Full text: PDF

Pages: 190-195

Published on: September 7, 2005
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Electronic Communications in Probability. ISSN: 1083-589X