论文标题
从马尔可夫进程到半明星
From Markov Processes to Semimartingales
论文作者
论文摘要
在随机整合和半明天的理论的发展中，马尔可夫过程一直是灵感的不断来源。尽管有这种历史的交织，但事实证明，对于马尔可夫框架中最初开发的许多概念，应将半明天被视为“自然”过程。例如，随机微分方程已被发明为研究马尔可夫过程的工具，但如今在文献中被分别处理。此外，几十年来，杀害过程已经闻名，直到最近才进入半明天的理论。我们描述了，何时在马尔可夫过程的理论中发明了这些和其他重要的概念，以及它们如何转移到半明天。其他主题包括Blumenthal-Getoor索引的符号，特征和概括。关于马尔可夫流程和半明星之间关系的一些其他评论阐明了论文。
In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the `natural' class of processes for many concepts first developed in the Markovian framework. As an example, stochastic differential equations have been invented as a tool to study Markov processes but nowadays are treated separately in the literature. Moreover, the killing of processes has been known for decades before it made its way to the theory of semimartingales most recently. We describe, when these and other important concepts have been invented in the theory of Markov processes and how they were transferred to semimartingales. Further topics include the symbol, characteristics and generalizations of Blumenthal-Getoor indices. Some additional comments on relations between Markov processes and semimartingales round out the paper.
