条件下确界与单调过程的恢复
Conditional infimum and recovery of monotone processes
摘要：
单调过程，就像鞅一样，经常可以从它们的最终值恢复。例子包括上鞅的运行极大值，以及运行极大值，局部时间和粘性过程的各种积分泛函，如分数布朗运动。一个有趣的推论是，任何正的局部鞅都可以由它的终值和它的全局极大值重构。这些结果依赖于条件下确界的概念，这是一个大类的完全格。该框架是足够普遍的处理也更奇特的例子，如过程的凸包的某些多维过程，和过程的网站访问的随机游动。
英文摘要：
Monotone processes, just like martingales, can often be recovered from their final values. Examples include running maxima of supermartingales, as well as running maxima, local times, and various integral functionals of sticky processes such as fractional Brownian motion. An interesting corollary is that any positive local martingale can be reconstructed from its final value and its global maximum. These results rely on the notion of conditional infimum, which is developed for a large class of complete lattices. The framework is sufficiently general to handle also more exotic examples, such as the process of convex hulls of certain multidimensional processes, and the process of sites visited by a random walk.
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。
