Decomposition of order statistics of semimartingales using local times
Abstract
In a recent work BG, given a collection of continuous semimartingales, authors derive a semimartingale decomposition from the corresponding ranked processes in the case that the ranked processes can meet more than two original processes at the same time. This has led to a more general decomposition of ranked processes. In this paper, we derive a more general result for semimartingales (not necessarily continuous) using a simpler approach. Furthermore, we also give a generalization of Ouknine O1, O2 and Yan's Y1 formula for local times of ranked processes
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