Our study aims to specify the asymptotic error distribution in the discretization of a stochastic Volterra equation with a fractional kernel. It is well-known that for a standard stochastic differential equation, the discretization error, normalized with its rate of convergence $1/\sqrt{n}$, converges in law to the solution of a certain linear equation. Similarly to this, we show that a suitably normalized discretization error of the Volterra equation converges in law to the solution of a certain linear Volterra equation with the same fractional kernel.

翻译：我们的研究旨在用一个分心内核分解的随机伏特拉方程式,具体说明无症状误差分布。众所周知,对于标准的随机差分方程式,离分差差差差,与其趋同率1美元/sqrt{n}美元,在法律上与某种线性方程式的解决方案趋同。与此类似,我们表明,Volterra方程式的适切、标准化离异差差差差在法律上与用同一分心内核的某一线性伏特拉方程式的解决方案相融合。