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半收缩漂移分数布朗运动驱动随机微分方程的平稳密度快速估计AI 解读

We study the estimation of the invariant density of additive fractional stochastic differential equations with Hurst parameter H∈(0,1). We first focus on continuous observations and develop a kernel-based estimator achieving faster convergence rates than previously available. This result stems from a martingale decomposition combined with new bounds on the (conditional) convergence in total variation to equilibrium of fractional SDEs. For H<1/2, we further refine the rates…

逐分量局部差分隐私约束下多元数据的极小极大速率AI 解读

Our research analyses the balance between maintaining privacy and preserving statistical accuracy when dealing with multivariate data that is subject to componentwise local differential privacy (CLDP). With CLDP, each component of the private data is made public through a separate privacy channel. This allows for varying levels of privacy protection for different components or for the privatization of each component by different entities, each with their own distinct privacy…