Article Dans Une Revue Proceeding of the Workshop on Mathematical Physic and Stochastic Analisys Année : 2000

Volterra differential equations with singular kernels

Laurent Decreusefond

Résumé

Motivated by the potential applications to the fractional Brownian motion, we study Volterra stochastic differential 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 Brownian motion and $(K(t,s), \, t,s \in [0,1])$ is a deterministic kernel whose properties will be precised below but for which we don't assume any boundedness property.

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hal-00265469 , version 1 (24-03-2017)

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Laure Coutin, Laurent Decreusefond. Volterra differential equations with singular kernels. Proceeding of the Workshop on Mathematical Physic and Stochastic Analisys, 2000, pp.1. ⟨hal-00265469⟩
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