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Research Paper#Nonlocal Equations, Lévy Measures, $L_p$ Estimates🔬 ResearchAnalyzed: Jan 3, 2026 16:39

$L_p$-estimates for Nonlocal Equations

Published:Dec 31, 2025 08:12
1 min read
ArXiv

Analysis

This paper investigates nonlocal operators, which are mathematical tools used to model phenomena that depend on interactions across distances. The authors focus on operators with general Lévy measures, allowing for significant singularity and lack of time regularity. The key contributions are establishing continuity and unique strong solvability of the corresponding nonlocal parabolic equations in $L_p$ spaces. The paper also explores the applicability of weighted mixed-norm spaces for these operators, providing insights into their behavior based on the parameters involved.
Reference

“The paper establishes continuity of the operators and the unique strong solvability of the corresponding nonlocal parabolic equations in $L_p$ spaces.”

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Research Paper#Stochastic Differential Equations, Lévy Noise, Least Squares Estimation, Sparse Data🔬 ResearchAnalyzed: Jan 3, 2026 18:21

Least Squares Estimation for SDEs with Lévy Noise and Sparse Data

Published:Dec 30, 2025 05:58
1 min read
ArXiv

Analysis

This paper addresses a practical problem in financial modeling and other fields where data is often sparse and noisy. The focus on least squares estimation for SDEs perturbed by Lévy noise, particularly with sparse sample paths, is significant because it provides a method to estimate parameters when data availability is limited. The derivation of estimators and the establishment of convergence rates are important contributions. The application to a benchmark dataset and simulation study further validate the methodology.
Reference

“The paper derives least squares estimators for the drift, diffusion, and jump-diffusion coefficients and establishes their asymptotic rate of convergence.”

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research#machine learning🔬 ResearchAnalyzed: Jan 4, 2026 06:48

Learning Lévy density via adaptive RKHS regression with bi-level optimization

Published:Dec 29, 2025 17:26
1 min read
ArXiv

Analysis

The article describes a research paper on a specific machine learning technique. The title indicates a focus on a mathematical concept (Lévy density) and a computational method (adaptive RKHS regression with bi-level optimization). The source, ArXiv, suggests this is a pre-print or research publication.
Reference

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