最优调谐泊松重启下随机过程的普适性质研究
On the universal properties of stochastic processes under optimally tuned Poisson restart
AI总结：
本文研究最优调谐泊松重启下随机过程的普适性质，发现了新的普适关系，并推导了多完成场景下完成时间二阶矩的普适不等式，拓展了随机过程重启优化的理论成果。
摘要：
泊松重启指随机过程在随机时刻被中断并重新启动的机制。已有诸多研究表明，该策略可缩短部分随机搜索任务的预期完成时间。此外，研究发现在最优重启速率下，任意随机过程无论其本质与统计细节如何，其完成时间的统计矩均满足若干普适关系。本文描述了最优重启过程的若干新普适性质，还针对存在多种可能完成场景的随机过程优化问题，推导得到了完成时间二阶统计矩的普适不等式。
英文摘要：
Poisson restart assumes that a stochastic process is interrupted and starts again at random time moments. A number of studies have demonstrated that this strategy may minimize the expected completion time in some classes of random search tasks. What is more, it turned out that under optimally tuned restart rate, any stochastic process, regardless of its nature and statistical details, satisfies a number of universal relations for the statistical moments of completion time. In this paper, we describe several new universal properties of optimally restarted processes. Also we obtain a universal inequality for the quadratic statistical moments of completion time in the optimization problem where stochastic process has several possible completion scenarios.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
