基于能量最优控制的跳跃奥恩斯坦-乌伦贝克桥及其自激扩展
A Jump Ornstein-Uhlenbeck Bridge Based on Energy-optimal Control and Its Self-exciting Extension
AI总结：
该研究基于带奇异终端条件的线性二次控制，构建了由谱正从属过程驱动、具显式表达式的跳跃奥恩斯坦-乌伦贝克桥及其自激扩展，验证了终端条件并应用于真实数据集的径流调节问题。
摘要：
我们研究了一类由谱正从属过程驱动的奥恩斯坦-乌伦贝克桥（Ornstein-Uhlenbeck bridge）。我们的构建基于带奇异终端条件的线性二次（Linear-Quadratic）控制。我们提出的奥恩斯坦-乌伦贝克桥被表示为所得最优控制过程的极限，且被证明具有显式表达式。我们还考虑了其带自激特性的扩展。我们通过解析和数值两种方式验证了所得过程满足终端条件。这些方法还被应用于基于真实数据集的径流调节问题。
英文摘要：
We study a version of the Ornstein-Uhlenbeck bridge driven by a spectrally-positive subordinator. Our formulation is based on a Linear-Quadratic control subject to a singular terminal condition. The Ornstein-Uhlenbeck bridge, we develop, is written as a limit of the obtained optimally controlled processes, and is shown to admit an explicit expression. Its extension with self-excitement is also considered. The terminal condition is confirmed to be satisfied by the obtained process both analytically and numerically. The methods are also applied to a streamflow regulation problem using a real-life dataset.
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。
