Peak Time-Windowed Risk Estimation of Stochastic Processes
CoRR(2024)
摘要
This paper develops a method to upper-bound extreme-values of time-windowed
risks for stochastic processes. Examples of such risks include the maximum
average or 90% quantile of the current along a transmission line in any
5-minute window. This work casts the time-windowed risk analysis problem as an
infinite-dimensional linear program in occupation measures. In particular, we
employ the coherent risk measures of the mean and the expected shortfall
(conditional value at risk) to define the maximal time-windowed risk along
trajectories. The infinite-dimensional linear program must then be truncated
into finite-dimensional optimization problems, such as by using the moment-sum
of squares hierarchy of semidefinite programs. The infinite-dimensional linear
program will have the same optimal value as the original nonconvex risk
estimation task under compactness and regularity assumptions, and the sequence
of semidefinite programs will converge to the true value under additional
properties of algebraic characterization. The scheme is demonstrated for
更多查看译文
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要