General Erased-Word Processes: Product-Type Filtrations, Ergodic Laws and Martin Boundaries
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2017
- DOI:
- 10.48550/arXiv.1712.00384
- arXiv:
- arXiv:1712.00384
- Bibcode:
- 2017arXiv171200384G
- Keywords:
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- Mathematics - Probability
- E-Print:
- Revised version