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.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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