Parabolic integro-differential nondegenerate Cauchy problem is considered in the scale of \(L_{p}\) spaces of functions whose regularity is defined by a Lévy measure with O-regularly varying radial profile. Existence and uniqueness of a solution is proved by deriving apriori estimates. Some probability density function estimates of the associated Lévy process are used as well.

中文翻译：

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径向O-正规变Lévy测度的随机积分-微分方程的柯西问题

在函数的\（L_ {p} \）空间的尺度上考虑抛物线积分微分非退化Cauchy问题，其规则性由具有O规则变化的径向轮廓的Lévy测度定义。通过推导先验估计来证明解决方案的存在性和唯一性。还使用了相关Lévy过程的一些概率密度函数估计。