In this paper, we develop an efficient nonparametric estimation theory for continuous time regression models with non-Gaussian Lévy noises in the case when the unknown functions belong to Sobolev ellipses. Using the Pinsker’s approach, we provide a sharp lower bound for the normalized asymptotic mean square accuracy. However, the main result obtained by Pinsker for the Gaussian white noise model is not correct without additional conditions for the ellipse coefficients. We find such constructive sufficient conditions under which we develop efficient estimation methods. We show that the obtained conditions hold for the ellipse coefficients of an exponential form. For exponential coefficients, the sharp lower bound is calculated in explicit form. Finally, we apply this result to signals number detection problems in multi-pass connection channels and we obtain an almost parametric convergence rate that is natural for this case, which significantly improves the rate with respect to power-form coefficients.

在未知函数属于Sobolev椭圆的情况下，本文针对非高斯Lévy噪声的连续时间回归模型开发了一种有效的非参数估计理论。使用Pinsker方法，我们为归一化渐近均方精度提供了一个尖锐的下界。但是，没有附加的椭圆系数条件，Pinsker对于高斯白噪声模型获得的主要结果是不正确的。我们发现了这样的建设性充分条件，可以在此条件下开发有效的估算方法。我们表明，获得的条件适用于指数形式的椭圆系数。对于指数系数，将以显式形式计算尖锐的下限。最后，