Exponential chi squared distributions in infinite ergodic theory

调节窗口化卡方检测器以应对传感器攻击

Tuning Windowed Chi-Squared Detectors for Sensor Attacks

本文提出基于模型的窗口化卡方方法用于识别伪造的传感器测量。通过静态卡方和动态累积和（CUSUM）故障检测方法比较窗口化卡方检测器的性能，分析攻击对系统状态退化的特征，并通过化工反应器仿真展示方法效果。

Counter-examples to the Dunford-Schwartz pointwise ergodic theorem on $L^1+L^\infty$

Extending a result by Chilin and Litvinov, we show by construction that given any $σ$-finite infinite measure space $(Ω,\mathcal{A}, μ)$ and a function $f\in L^1(Ω)+L^\infty(Ω)$ with $μ(\{|f|>\varepsilon\})=\infty$ for some $\varepsilon>0$, there exists a Dunford-Schwartz operator $T$ over $(Ω,\mathcal{A}, μ)$ such that $\frac{1}{N}\sum_{n=1}^N (T^nf)(x)$ fails to converge for almost every $x\inΩ$. In addition, for each operator we construct, the set of functions for which pointwise convergence fails almost everywhere is residual in $L^1(Ω)+L^\infty(Ω)$.