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arXiv · 1712.00384

General Erased-Word Processes: Product-Type Filtrations, Ergodic Laws and Martin Boundaries

Julian Gerstenberg
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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 S.Laurent.

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Julian Gerstenberg. 2017-12-01. General Erased-Word Processes: Product-Type Filtrations, Ergodic Laws and Martin Boundaries. https://arxiv.org/abs/1712.00384

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