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.
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