A class of (possibly) degenerate integro-differential equations of parabolic type is considered, which includes the Kolmogorov equations for jump diffusions. Existence and uniqueness of the solutions are established in Bessel potential spaces and in Sobolev-Slobodeckij spaces. Generalisations to stochastic integro-differential equations, arising in filtering theory of jump diffusions, will be given in a forthcoming paper.

中文翻译：

---

积分微分方程的可解性

考虑了一类（可能）简并的抛物型积分微分方程，其中包括用于跳扩散的Kolmogorov方程。在Bessel势空间和Sobolev-Slobodeckij空间中建立了解的存在性和唯一性。将在即将发表的论文中给出对随机积分微分方程的一般化，其由跳跃扩散的滤波理论引起。