中文摘要：

研究了1类带有Goursat型核函数保留了维纳测度的Volterra变换,这类核函数满足自再生性.给出了几个能引起新的自再生性的相关Gram矩阵逆的结果,以及它与经典自再生性的联系.结果被应用于1类带相应滤过分解的奇异线性随机微分方程研究,研究的方程被看作是一些广义桥的非标准分解.

英文摘要：

The type with Goursat kernel function retained the Wiener measure on the Volterra transformation is studied. This kind of kernel function satisfy a self-reproduction property. Some results on the inverses of the associated Gramian matrices which lead to a new self-reproduction property are provided. And it links with the classical reproduction property. The result is applied to a class of singular linear stochastic differential equation with corresponding filter decomposition＇s study. The equation is regarded as some non-standard decomposition of generalized bridges.