Author

E. Moldavskaya

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Preprint Sep 2026

Malliavin Smoothness of Hermite Processes of Arbitrary Order and Their Wiener Integrals

We establish Malliavin nondegeneracy for every weighted integral against a singular Hermite kernel, with all negative moments of the Malliavin derivative norm finite, uniformly over admissible compact families of bounded deterministic weights. In particular, all finite-dimensional distributions of Hermite processes of...

E. Moldavskaya · 0 citations

Preprint Sep 2026

Malliavin smoothness and density estimates for the third-order Hermite process

We prove Malliavin nondegeneracy for the third-order Hermite process. The key step is to show that, for every nonzero test direction $h\in C_c^\infty(0,1)$, the directional Malliavin derivative of a third-order Hermite random variable is an infinite-rank Gaussian quadratic form. Using arbitrarily large orthonormal fami...

E. Moldavskaya · 1 citation · ⚡1

#machine learning Preprint Sep 2026

Weighted Empirical Risk Minimization for Machine Learning under Long-Range Dependence: Exact Pathwise Rates and Learning-Error Geometry

We develop an exact almost-sure learning theory for smooth parametric models trained by regularly weighted empirical risk minimization on long-range dependent data. The training observations are generated from a fixed finite window of a stationary Gaussian sequence, and the sample weights are regularly varying. If the...

E. Moldavskaya · 1 citation