Perfect Simulation and Convex Mixture of Context Trees

Garcia, Nancy L.; Gallo, Sandro

doi:10.1007/978-3-319-94015-1_7

Cited by 2 publications

(2 citation statements)

References 29 publications

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“…Gallo and Paccaut (2013), (see corollary 1 and example 4 therein) need the parameter to be sufficiently large to compensate the exponential growth of the set of discontinuities. This is also the case of Garcia and Gallo (2018) which relies on the results of Gallo and Paccaut (2013). Gallo (2011) and Gallo and Garcia (2013) on the other hand obtained existence adding a condition on the continuity set X − \D g which is rather strong and in particular implies also uniqueness.…”

Section: Explicit Results: Using the Form Of D Gmentioning

confidence: 89%

Non-regular g-measures and variable length memory chains

2020

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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 a 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 dedicated to the case of variable length memory chains, for which we obtain existence, uniqueness and weak-Bernoullicity (or β-mixing) under new assumptions. These results are specially designed for variable length memory models, and do not require uniform continuity. We also provide a further discussion on some related notions, such as random context processes, non-essential discontinuities and everywhere discontinuous stationary measures.

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Section: Explicit Results: Using the Form Of D Gmentioning

confidence: 89%

Non-regular g-measures and variable length memory chains

2020

Self Cite

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“…Gallo & Paccaut (2013, see Corollary 1 and Example 4 therein) need the parameter ǫ to be sufficiently large to compensate the exponential growth of the set of discontinuities (see definitions therein). This is also the case of Garcia & Gallo (2018) which relies on the results of Gallo & Paccaut (2013). Gallo (2011) and Gallo & Garcia (2013) on the other hand obtained existence adding a condition on the continuity set X − \ D g which is rather strong and in particular implies also uniqueness.…”

Section: 6mentioning

confidence: 89%

Non-regular g-measures and variable length memory chains

Ferreira,

Gallo,

Paccaut

2019

Preprint

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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 β-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.

show abstract

Perfect Simulation and Convex Mixture of Context Trees

Cited by 2 publications

References 29 publications

Non-regular g-measures and variable length memory chains

Non-regular g-measures and variable length memory chains

Non-regular g-measures and variable length memory chains

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