Volterra differential equations with singular kernels
Coutin, Laure ; Decreusefond, Laurent
HAL, hal-00265469 / Harvested from HAL
Text on HAL
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.
Publié le : 2000-07-04
Classification:  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00265469,
     author = {Coutin, Laure and Decreusefond, Laurent},
     title = {Volterra differential equations with singular kernels},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00265469}
}

Coutin, Laure; Decreusefond, Laurent. Volterra differential equations with singular kernels. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00265469/