Original article at: http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=1741

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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Original article at: http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=1741