Fischer, Tom On simple representations of stopping times and stopping time sigma-algebras. (English) Zbl 1260.60075 Stat. Probab. Lett. 83, No. 1, 345-349 (2013). Summary: There exists a simple, didactically useful one-to-one relationship between stopping times and adapted càdlàg (RCLL) processes that are non-increasing and take the values 0 and 1 only. As a consequence, stopping times are always hitting times. Furthermore, we show how minimal elements of a stopping time sigma-algebra can be expressed in terms of the minimal elements of the sigma-algebras of the underlying filtration. This facilitates an intuitive interpretation of stopping time sigma-algebras. A tree example finally illustrates how these for students notoriously difficult concepts, stopping times and stopping time sigma-algebras, may be easier to grasp by means of our results. Cited in 3 Documents MSC: 60G40 Stopping times; optimal stopping problems; gambling theory 97K50 Probability theory (educational aspects) 97K60 Distributions and stochastic processes (educational aspects) Keywords:début theorem; hitting time; stopped sigma-algebra; stopping time; stopping time sigma-algebra PDFBibTeX XMLCite \textit{T. Fischer}, Stat. Probab. Lett. 83, No. 1, 345--349 (2013; Zbl 1260.60075) Full Text: DOI arXiv arXiv