Volterra differential equations with singular kernels

Laure Coutin; Laurent Decreusefond

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arXiv · 1703.08395

Volterra differential equations with singular kernels

Laure Coutin·Laurent Decreusefond

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Abstract

Motivated by the potential applications to the fractional Brownianmotion, we study Volterra stochasticdifferential of the form~:\begin{equation}X\_t = x+ \int\_0^tK(t,s)b(s,X\_s)ds + \int\_0^tK(t,s) \sigma(s,X\_s)\,dB\_s ,\tag{E} \label{eq:sdefbm}\end{equation}where $(B\_s, \, s\in [0,1])$ is a one-dimensional standard Brownianmotion and $(K(t,s), \, t,s \in [0,1])$ is a deterministic kernelwhose properties will be precised below but for which we don't assumeany boundedness property.

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Laure Coutin, Laurent Decreusefond. 2017-03-24. Volterra differential equations with singular kernels. https://arxiv.org/abs/1703.08395

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