On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients

Stadlbauer, Manuel; Zhang, Xuan

doi:10.1088/1361-6544/abd7c5

Cited by 4 publications

(7 citation statements)

References 21 publications

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“…is can verify the feasibility of problem transformation in this task and the effectiveness of adding legal provisions [18].…”

Section: Results Analysismentioning

confidence: 97%

Evidence Prediction Method Based on Sentence Selection for Legal Documents

Bai

2022

Advances in Multimedia

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In order to solve the problem that it is difficult to find evidence from a large number of legal document statements and the irrelevant statements in a large number of document sample data will cause a great interference to the prediction results and further improve the accuracy of evidence prediction, this paper puts forward an intelligent evidence criterion prediction method for legal documents based on the comprehensive consideration of legal problems, the nature of statements, and the characteristics of answers. The binary cross-entropy of different statements is used to obtain the interaction information between different statements. Through experiments, it is found that the score of Joint F1 proposed in this paper is 70.07%, which is more accurate than the mainstream model and also verifies the effectiveness of the scheme.

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“…is can verify the feasibility of problem transformation in this task and the effectiveness of adding legal provisions [18].…”

Section: Results Analysismentioning

confidence: 97%

Evidence Prediction Method Based on Sentence Selection for Legal Documents

Bai

2022

Advances in Multimedia

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“…The almost sure invariance principle we are going to show is similar to the one in [32] for non-stationary shift. Both are based on the almost sure invariance principle for reverse martingale differences by Cuny and Merlevède.…”

Section: Dρ(ω)mentioning

confidence: 59%

“…A further application of Theorem A is related to an invariance principle as the contraction allows us to apply the general invariance principle in [10] and gives rise to the following result (for a similar result for continued fractions with restricted entries, see [32]). Here, [ω] n stands for the initial n-word of an infinite word ω. THEOREM B.…”

Section: Statement Of the Main Resultsmentioning

confidence: 95%

Quenched and annealed equilibrium states for random Ruelle expanding maps and applications

Stadlbauer

Varandas

Zhang³

2022

Ergod. Th. Dynam. Sys.

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We find generalized conformal measures and equilibrium states for random dynamics generated by Ruelle expanding maps, under which the dynamics exhibits exponential decay of correlations. This extends results by Baladi [Correlation spectrum of quenched and annealed equilibrium states for random expanding maps. Comm. Math. Phys.186 (1997), 671–700] and Carvalho et al [Semigroup actions of expanding maps. J. Stat. Phys.116(1) (2017), 114–136], where the randomness is driven by an independent and identically distributed process and the phase space is assumed to be compact. We give applications in the context of weighted non-autonomous iterated function systems, free semigroup actions and introduce a boundary of equilibria for not necessarily free semigroup actions.

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“…As shown in [BS16,SZ17], this estimate and the fact that X is a full shift allows to deduce the following. With respect to the equivalent metric…”

Section: Perron-frobenius-ruelle Theoremmentioning

confidence: 67%

“…, where d is the Wasserstein metric on the space of probability measures as defined in (2) (see Theorem 1.1.5 in [BK12]). Note that (7) is also known as geometric ergodicity in the literature on probability theory and that geometric ergodicity was established in [Sta17,BS16,SZ17] for non-stationary and random countable shift spaces.…”

Section: N})mentioning

confidence: 99%

Thermodynamic formalism for topological Markov chains on standard Borel spaces

Cioletti¹,

Silva²,

Stadlbauer³

2019

Discrete &Amp; Continuous Dynamical Systems - A

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We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space X ≡ E N , where E is a general standard Borel space. In particular, we introduce meaningful concepts of entropy and pressure for shifts acting on X and obtain the existence of equilibrium states as finitely additive probability measures for any bounded continuous potential. Furthermore, we establish convexity and other structural properties of the set of equilibrium states, prove a version of the Perron-Frobenius-Ruelle theorem under additional assumptions on the regularity of the potential and show that the Yosida-Hewitt decomposition of these equilibrium states does not have a purely finite additive part.We then apply our results to the construction of invariant measures of timehomogeneous Markov chains taking values on a general Borel standard space and obtain exponential asymptotic stability for a class of Markov operators. We also construct conformal measures for an infinite collection of interacting random paths which are associated to a potential depending on infinitely many coordinates. Under an additional differentiability hypothesis, we show how this process is related after a proper scaling limit to a certain infinite-dimensional diffusion.2010 Mathematics Subject Classification. 37D35, 28Dxx.

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On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients

Cited by 4 publications

References 21 publications

Evidence Prediction Method Based on Sentence Selection for Legal Documents

Evidence Prediction Method Based on Sentence Selection for Legal Documents

Quenched and annealed equilibrium states for random Ruelle expanding maps and applications

Thermodynamic formalism for topological Markov chains on standard Borel spaces

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