Open Access
2016 Geometry of stochastic delay differential equations with jumps in manifolds
Paulo R. Ruffino, Leandro Morgado
Electron. Commun. Probab. 21: 1-9 (2016). DOI: 10.1214/16-ECP4764


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. In the last section, using a geometrical approach, 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 horizontal connection $\nabla ^H$ in $BM$.


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Paulo R. Ruffino. Leandro Morgado. "Geometry of stochastic delay differential equations with jumps in manifolds." Electron. Commun. Probab. 21 1 - 9, 2016.


Received: 16 December 2015; Accepted: 15 April 2016; Published: 2016
First available in Project Euclid: 28 April 2016

zbMATH: 1338.60150
MathSciNet: MR3510245
Digital Object Identifier: 10.1214/16-ECP4764

Primary: 34K50 , 53C05 , 60H10

Keywords: linear frame bundle , parallel transport , stochastic delay differential equations , Stochastic differential equations with jumps , Stochastic geometry

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