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arXiv · 1503.05772

Stochastic delay differential equations with jumps in differentiable manifolds

Leandro Morgado·Paulo R. Ruffino
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Abstract

In this article we propose a model for stochastic delay differential equation with jumps (SDDEJ) in a differentiable manifold $M$ endowed with a connection $\nabla$. In our model, the continuous part is driven by vector fields with a fixed delay and the jumps are assumed to come from a distinct source of (càdlàg) noise, without delay. The jumps occur along adopted differentiable curves with some dynamical relevance (with fictitious time) which allow to take parallel transport along them. Using a geometrical approach, in the last section, we show that the horizontal lift of the solution of an SDDEJ is again a solution of an SDDEJ in the linear frame bundle $BM$ with respect to a connection $\nabla^H$ in $BM$.

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BibTeXRIS

Leandro Morgado, Paulo R. Ruffino. 2015-03-19. Stochastic delay differential equations with jumps in differentiable manifolds. https://arxiv.org/abs/1503.05772

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