Volterra differential equations with singular kernels
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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