The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Dans cet article, nous considérons une approche basée sur le tenseur pour le calcul analytique des attentes d'ordre supérieur de trajectoires quantifiées générées par des cartes de Markov affine par morceaux (PWAM). Nous dérivons formellement des expressions de forme fermée pour les attentes de trajectoires générées par trois familles de cartes, appelées (n,t)-décalages à queue, (n,t)-identités brisées et (n,t,π)-permutations de mélange. Ces familles produisent des attentes à décroissance exponentielle asymptotique dont le profil détaillé est contrôlé par la conception de la carte. Dans le (n,tLes attentes des cas de décalage à queue ) alternent en signe, dans le (n,t)-cas d'identité brisée, ils sont de signe constant, et le (n,t,π)-dans le cas de permutation de mélange, ils suivent une tendance périodique sous-évaluée.
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Gianluca SETTI, Riccardo ROVATTI, Gianluca MAZZINI, "Tensor-Based Theory for Quantized Piecewise-Affine Markov Systems: Analysis of Some Map Families" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 9, pp. 2090-2100, September 2001, doi: .
Abstract: In this paper we consider a tensor-based approach to the analytical computation of higher-order expectations of quantized trajectories generated by Piecewise Affine Markov (PWAM) maps. We formally derive closed-form expressions for expectations of trajectories generated by three families of maps, referred to as (n,t)-tailed shifts, (n,t)-broken identities and (n,t,π)-mixing permutations. These families produce expectations with asymptotic exponential decay whose detailed profile is controlled by map design. In the (n,t)-tailed shift case expectations are alternating in sign, in the (n,t)-broken identity case they are constant in sign, and the (n,t,π)-mixing permutation case they follow a dumped periodic trend.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_9_2090/_p
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@ARTICLE{e84-a_9_2090,
author={Gianluca SETTI, Riccardo ROVATTI, Gianluca MAZZINI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Tensor-Based Theory for Quantized Piecewise-Affine Markov Systems: Analysis of Some Map Families},
year={2001},
volume={E84-A},
number={9},
pages={2090-2100},
abstract={In this paper we consider a tensor-based approach to the analytical computation of higher-order expectations of quantized trajectories generated by Piecewise Affine Markov (PWAM) maps. We formally derive closed-form expressions for expectations of trajectories generated by three families of maps, referred to as (n,t)-tailed shifts, (n,t)-broken identities and (n,t,π)-mixing permutations. These families produce expectations with asymptotic exponential decay whose detailed profile is controlled by map design. In the (n,t)-tailed shift case expectations are alternating in sign, in the (n,t)-broken identity case they are constant in sign, and the (n,t,π)-mixing permutation case they follow a dumped periodic trend.},
keywords={},
doi={},
ISSN={},
month={September},}
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TY - JOUR
TI - Tensor-Based Theory for Quantized Piecewise-Affine Markov Systems: Analysis of Some Map Families
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2090
EP - 2100
AU - Gianluca SETTI
AU - Riccardo ROVATTI
AU - Gianluca MAZZINI
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2001
AB - In this paper we consider a tensor-based approach to the analytical computation of higher-order expectations of quantized trajectories generated by Piecewise Affine Markov (PWAM) maps. We formally derive closed-form expressions for expectations of trajectories generated by three families of maps, referred to as (n,t)-tailed shifts, (n,t)-broken identities and (n,t,π)-mixing permutations. These families produce expectations with asymptotic exponential decay whose detailed profile is controlled by map design. In the (n,t)-tailed shift case expectations are alternating in sign, in the (n,t)-broken identity case they are constant in sign, and the (n,t,π)-mixing permutation case they follow a dumped periodic trend.
ER -