General erased-word processes: Product-type filtrations, ergodic laws and Martin boundaries

Julian Gerstenberg

Stochastic Processes and their Applications, 2020, vol. 130, issue 6, 3540-3573

Abstract: We study the dynamics of erasing randomly chosen letters from words by introducing a certain class of discrete-time stochastic processes, general erased-word processes (GEWPs), and investigating three closely related topics: Representation, Martin boundary and filtration theory. We use de Finetti’s theorem and the random exchangeable linear order to obtain a de Finetti-type representation of GEWPs involving induced order statistics. Our studies expose connections between exchangeability theory and certain poly-adic filtrations that can be found in other exchangeable random objects as well. We show that ergodic GEWPs generate backward filtrations of product-type and by that generalize a result by Laurent (2016).

Keywords: Exchangeability; Simplex; Poly-adic filtration; Martin boundary; Coupling method; Induced order statistics (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.10.003

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