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

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  • Gerstenberg, Julian

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).

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  • Gerstenberg, Julian, 2020. "General erased-word processes: Product-type filtrations, ergodic laws and Martin boundaries," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3540-3573.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:6:p:3540-3573
    DOI: 10.1016/j.spa.2019.10.003
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    1. Choi, Hye Soo & Evans, Steven N., 2017. "Doob–Martin compactification of a Markov chain for growing random words sequentially," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2428-2445.
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