Non-regular g-measures and variable length memory chains
| Autor: | Ricardo F. Ferreira, Frédéric Paccaut, Sandro Gallo |
|---|---|
| Přispěvatelé: | Instituto de Matemática da Universidade Federal do Rio de Janeiro (IM / UFRJ), Universidade Federal do Rio de Janeiro (UFRJ), Laboratoire Amiénois de Mathématique Fondamentale et Appliquée (LAMFA), Université de Picardie Jules Verne (UPJV)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Applied Mathematics 010102 general mathematics Null (mathematics) Probability (math.PR) General Physics and Astronomy Statistical and Nonlinear Physics Context (language use) Classification of discontinuities Variable length 01 natural sciences Measure (mathematics) 010101 applied mathematics Set (abstract data type) [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Uniform continuity 60J05 37E05 FOS: Mathematics Uniqueness 0101 mathematics Mathematical Physics Mathematics - Probability Mathematics |
| DOI: | 10.48550/arxiv.1907.02442 |
| Popis: | It is well-known that there always exists at least one stationary measure compatible with a continuous g-function g. Here we prove that if the set of discontinuities of the g-function g has null measure under a candidate measure obtained by some asymptotic procedure, then this candidate measure is compatible with g. We explore several implications of this result, and discuss comparisons with the literature concerning assumptions and examples. Important part of the paper is concerned with the case of variable length memory chains, for which we obtain existence, uniqueness and weak-Bernoullicity (or $\beta$-mixing) under new assumptions. These results are specially designed for variable length memory models, and do not require vanishing uniform variation. We also provide a further discussion on some related notions, such as random context processes, non-essential discontinuities, and finally an example of everywhere discontinuous stationary measure. Comment: 33 pages |
| Databáze: | OpenAIRE |
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