We study high-dimensional Ornstein--Uhlenbeck processes driven by Lévy noise and consider drift matrices that decompose into a low-rank plus sparse component, capturing a few latent factors together with a sparse network of direct interactions. For discrete-time observations under the localized, truncated contrast of Dexheimer and Jeszka, we analyze a convex estimator that minimizes this contrast with a combined nuclear-norm and $\ell_1$-penalty on the low-rank and sparse parts, respectively. Under a restricted strong convexity condition, a rank--sparsity incoherence assumption, and regime-specific choices of truncation level, horizon, and sampling mesh for the background driving Lévy process, we derive a non-asymptotic oracle inequality for the Frobenius risk of the estimator. The bound separates a discretization bias term of order $d^2Δ_n^2$ from a stochastic term of order $γ(Δ_n)T^{-1}(r \log d + s \log d)$, thereby showing that the low-rank-plus-sparse structure improves the dependence on the ambient dimension relative to purely sparse estimators while retaining the same discretization and truncation behavior across the four Lévy regimes.

翻译：我们研究由Lévy噪声驱动的高维Ornstein--Uhlenbeck过程，并考虑将漂移矩阵分解为低秩分量与稀疏分量之和，以捕捉少数潜在因子及直接相互作用的稀疏网络。针对Dexheimer和Jeszka提出的局部化截断对比度下的离散时间观测，我们分析了一种凸估计器，该估计器通过分别对低秩部分和稀疏部分施加核范数与$\ell_1$惩罚项的组合来最小化此对比度。在受限强凸性条件、秩-稀疏性不相干假设，以及针对背景驱动Lévy过程的截断水平、时间跨度和采样网格的特定区域选择下，我们推导了该估计器Frobenius风险的非渐近Oracle不等式。该界将阶数为$d^2Δ_n^2$的离散化偏差项与阶数为$γ(Δ_n)T^{-1}(r \log d + s \log d)$的随机项分离，从而表明：相较于纯稀疏估计器，低秩加稀疏结构改善了其对环境维度的依赖性，同时在四种Lévy区域中保持了相同的离散化与截断行为。