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Brownian local minima, random dense countable sets and random equivalence classes. (English) Zbl 1112.60065

Summary: A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are ‘Brownian local minima’ and ‘unordered infinite sample’. They are identically distributed. A framework for such concepts, proposed here, includes a wide class of random equivalence classes.

MSC:

60J65 Brownian motion
60Gxx Stochastic processes
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