Volterra differential equations with singular kernels (1703.08395v1)

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.