On a dyadic approximation of predictable processes of finite variation

2013/06/26 by Pietro Siorpaes, Siorpaes, Pietro
Arts and Humanities · Engineering · Mathematics · #60G07 #60G40 #60G44 #FOS: Mathematics #Philosophy and History of Science #Probability (math.PR) #Reservoir Engineering and Simulation Methods #Statistical Methods in Clinical Trials

paper · pdf · doi:10.48550/arxiv.1306.6238

openalex publication_date 2013/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that any cadlag predictable process of finite variation is an a.s. limit of elementary predictable processes; it follows that predictable stopping times can be approximated `from below' by predictable stopping times which take finitely many values. We then obtain as corollaries two classical theorems: predictable stopping times are announceable, and an increasing process is predictable iff it is natural.

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