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Journal articles on the topic 'Ergodicité'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2025

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1

Mokkadem, Abdelkader. "SUR UN MODÉLE AUTORÉGRESSIF NON LINÉAIRE, ERGODICITÉ ET ERGODICITÉ GÉOMÉTRIQUE." Journal of Time Series Analysis 8, no. 2 (March 1987): 195–204. http://dx.doi.org/10.1111/j.1467-9892.1987.tb00432.x.

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2

Cépa, E., and s. Jacquot. "Ergodicité d'inégalités variationnelles stochastiques." Stochastics and Stochastic Reports 63, no. 1-2 (April 1998): 41–64. http://dx.doi.org/10.1080/17442509808834142.

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3

Tricot, Claude, and Rudolf Riedi. "Attracteurs, orbites et ergodicité." Annales mathématiques Blaise Pascal 6, no. 1 (1999): 55–72. http://dx.doi.org/10.5802/ambp.115.

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4

Muraz. "ERGODICITÉ ET FONCTIONS DE RIEMANN." Real Analysis Exchange 21, no. 1 (1995): 84. http://dx.doi.org/10.2307/44153889.

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5

Leoncini, Xavier, Cristel Chandre, and Ouerdia Ourrad. "Ergodicité, collage et transport anomal." Comptes Rendus Mécanique 336, no. 6 (June 2008): 530–35. http://dx.doi.org/10.1016/j.crme.2008.02.006.

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6

Roblin, Thomas. "Ergodicité et équidistribution en courbure négative." Mémoires de la Société mathématique de France 1 (2003): 1–96. http://dx.doi.org/10.24033/msmf.408.

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7

Üstünel, Ali Süleyman, and Moshe Zakai. "Ergodicité des rotations sur l'espace de Wiener." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 330, no. 8 (April 2000): 725–28. http://dx.doi.org/10.1016/s0764-4442(00)00249-4.

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8

Parreau, François. "Ergodicité et pureté des produits de Riesz." Annales de l’institut Fourier 40, no. 2 (1990): 391–405. http://dx.doi.org/10.5802/aif.1218.

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9

MAURIN, M. "La transformation logarithme des processus stochastiques, ergodicité." Le Journal de Physique IV 04, no. C5 (May 1994): C5–1353—C5–1356. http://dx.doi.org/10.1051/jp4:19945301.

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10

Buzzi, Jérôme. "Ergodicité intrinsèque de produits fibrés d'applications chaotiques unidimensionnelles." Bulletin de la Société mathématique de France 126, no. 1 (1998): 51–77. http://dx.doi.org/10.24033/bsmf.2320.

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11

Besson, Gérard. "Ergodicité du flot géodésique des surfaces riemanniennes à courbure -1." Séminaire de théorie spectrale et géométrie S9 (1991): 25–31. http://dx.doi.org/10.5802/tsg.109.

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12

Coornaert, M., and A. Papadoppoulos. "Récurrence des marches aléatoires et ergodicité du flot géodésique sur les graphes réguliers." MATHEMATICA SCANDINAVICA 79 (June 1, 1996): 130. http://dx.doi.org/10.7146/math.scand.a-12596.

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13

Bouzouina, Abdelkader, and Stephan De Bièvre. "Equidistribution des valeurs propres et ergodicité semi-classique de symplectomorphismes du tore quantifiés." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, no. 8 (April 1998): 1021–24. http://dx.doi.org/10.1016/s0764-4442(98)80134-1.

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14

Boussama, Farid. "Ergodicité des chaînes de Markov à valeurs dans une variété algébrique : application aux modèles GARCH multivariés." Comptes Rendus Mathematique 343, no. 4 (August 2006): 275–78. http://dx.doi.org/10.1016/j.crma.2006.06.027.

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15

Kolesnikova, Kateryna, Тetyana Olekh, Yulia Barchanova, and Valentyna Vasilieva. "Ergodicity of project management system." Odes’kyi Politechnichnyi Universytet. Pratsi, no. 3 (December 23, 2015): 46–50. http://dx.doi.org/10.15276/opu.3.47.2015.12.

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16

ZHOU, Yunhua. "Robust Weak Ergodicity And Stable Ergodicity." Acta Mathematica Scientia 33, no. 5 (September 2013): 1375–81. http://dx.doi.org/10.1016/s0252-9602(13)60088-0.

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17

Hou, Zhenting, and Yuanyuan Liu. "Explicit criteria for several types of ergodicity of the embedded M/G/1 and GI/M/n queues." Journal of Applied Probability 41, no. 3 (September 2004): 778–90. http://dx.doi.org/10.1239/jap/1091543425.

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This paper investigates the rate of convergence to the probability distribution of the embedded M/G/1 and GI/M/n queues. We introduce several types of ergodicity including l-ergodicity, geometric ergodicity, uniformly polynomial ergodicity and strong ergodicity. The usual method to prove ergodicity of a Markov chain is to check the existence of a Foster–Lyapunov function or a drift condition, while here we analyse the generating function of the first return probability directly and obtain practical criteria. Moreover, the method can be extended to M/G/1- and GI/M/1-type Markov chains.

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18

Hou, Zhenting, and Yuanyuan Liu. "Explicit criteria for several types of ergodicity of the embedded M/G/1 and GI/M/n queues." Journal of Applied Probability 41, no. 03 (September 2004): 778–90. http://dx.doi.org/10.1017/s0021900200020544.

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This paper investigates the rate of convergence to the probability distribution of the embedded M/G/1 and GI/M/n queues. We introduce several types of ergodicity including l-ergodicity, geometric ergodicity, uniformly polynomial ergodicity and strong ergodicity. The usual method to prove ergodicity of a Markov chain is to check the existence of a Foster–Lyapunov function or a drift condition, while here we analyse the generating function of the first return probability directly and obtain practical criteria. Moreover, the method can be extended to M/G/1- and GI/M/1-type Markov chains.

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19

Hordijk, Arie, and Flora Spieksma. "On ergodicity and recurrence properties of a Markov chain by an application to an open jackson network." Advances in Applied Probability 24, no. 02 (June 1992): 343–76. http://dx.doi.org/10.1017/s000186780004756x.

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This paper gives an overview of recurrence and ergodicity properties of a Markov chain. Two new notions for ergodicity and recurrence are introduced. They are calledμ-geometric ergodicity andμ-geometric recurrence respectively. The first condition generalises geometric as well as strong ergodicity. Our key theorem shows thatμ-geometric ergodicity is equivalent to weakμ-geometric recurrence. The latter condition is verified for the time-discretised two-centre open Jackson network. Hence, the corresponding two-dimensional Markov chain isμ-geometrically and geometrically ergodic, but not strongly ergodic. A consequence ofμ-geometric ergodicity withμof product-form is the convergence of the Laplace-Stieltjes transforms of the marginal distributions. Consequently all moments converge.

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20

Borovkov, A. A., and A. Hordijk. "Characterization and sufficient conditions for normed ergodicity of Markov chains." Advances in Applied Probability 36, no. 1 (March 2004): 227–42. http://dx.doi.org/10.1239/aap/1077134471.

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Normed ergodicity is a type of strong ergodicity for which convergence of the nth step transition operator to the stationary operator holds in the operator norm. We derive a new characterization of normed ergodicity and we clarify its relation with exponential ergodicity. The existence of a Lyapunov function together with two conditions on the uniform integrability of the increments of the Markov chain is shown to be a sufficient condition for normed ergodicity. Conversely, the sufficient conditions are also almost necessary.

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21

Borovkov, A. A., and A. Hordijk. "Characterization and sufficient conditions for normed ergodicity of Markov chains." Advances in Applied Probability 36, no. 01 (March 2004): 227–42. http://dx.doi.org/10.1017/s0001867800012945.

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Normed ergodicity is a type of strong ergodicity for which convergence of thenth step transition operator to the stationary operator holds in the operator norm. We derive a new characterization of normed ergodicity and we clarify its relation with exponential ergodicity. The existence of a Lyapunov function together with two conditions on the uniform integrability of the increments of the Markov chain is shown to be a sufficient condition for normed ergodicity. Conversely, the sufficient conditions are also almost necessary.

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22

Hordijk, Arie, and Flora Spieksma. "On ergodicity and recurrence properties of a Markov chain by an application to an open jackson network." Advances in Applied Probability 24, no. 2 (June 1992): 343–76. http://dx.doi.org/10.2307/1427696.

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This paper gives an overview of recurrence and ergodicity properties of a Markov chain. Two new notions for ergodicity and recurrence are introduced. They are called μ -geometric ergodicity and μ -geometric recurrence respectively. The first condition generalises geometric as well as strong ergodicity. Our key theorem shows that μ -geometric ergodicity is equivalent to weak μ -geometric recurrence. The latter condition is verified for the time-discretised two-centre open Jackson network. Hence, the corresponding two-dimensional Markov chain is μ -geometrically and geometrically ergodic, but not strongly ergodic. A consequence of μ -geometric ergodicity with μ of product-form is the convergence of the Laplace-Stieltjes transforms of the marginal distributions. Consequently all moments converge.

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23

Liu, Lee R., Dina Rosenberg, P. Bryan Changala, Philip J. D. Crowley, David J. Nesbitt, Norman Y. Yao, Timur V. Tscherbul, and Jun Ye. "Ergodicity breaking in rapidly rotating C ₆₀ fullerenes." Science 381, no. 6659 (August 18, 2023): 778–83. http://dx.doi.org/10.1126/science.adi6354.

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Ergodicity, the central tenet of statistical mechanics, requires an isolated system to explore all available phase space constrained by energy and symmetry. Mechanisms for violating ergodicity are of interest for probing nonequilibrium matter and protecting quantum coherence in complex systems. Polyatomic molecules have long served as a platform for probing ergodicity breaking in vibrational energy transport. Here, we report the observation of rotational ergodicity breaking in an unprecedentedly large molecule, 12 C 60 , determined from its icosahedral rovibrational fine structure. The ergodicity breaking occurs well below the vibrational ergodicity threshold and exhibits multiple transitions between ergodic and nonergodic regimes with increasing angular momentum. These peculiar dynamics result from the molecule’s distinctive combination of symmetry, size, and rigidity, highlighting its relevance to emergent phenomena in mesoscopic quantum systems.

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24

Rahimi, M., and A. Assari. "Ergodicity Space for Measure-Preserving Transformations." Chinese Journal of Mathematics 2016 (August 21, 2016): 1–5. http://dx.doi.org/10.1155/2016/6274839.

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We introduce the concept of ergodicity space of a measure-preserving transformation and will present some of its properties as an algebraic weight for measuring the size of the ergodicity of a measure-preserving transformation. We will also prove the invariance of the ergodicity space under conjugacy of dynamical systems.

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25

Pugh, Charles, Michael Shub, and an appendix by Alexander Starkov. "Stable ergodicity." Bulletin of the American Mathematical Society 41, no. 01 (November 4, 2003): 1–42. http://dx.doi.org/10.1090/s0273-0979-03-00998-4.

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26

Zheng, Zuohuan. "Generalized ergodicity." Science in China Series A: Mathematics 44, no. 9 (September 2001): 1098–106. http://dx.doi.org/10.1007/bf02877426.

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27

Spieksma, F. M., and R. L. Tweedie. "Strengthening ergodicity to geometric ergodicity for markov chains." Communications in Statistics. Stochastic Models 10, no. 1 (January 1994): 45–74. http://dx.doi.org/10.1080/15326349408807288.

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28

Xu, XIA, ZHENG ZuoHuan, and ZHOU Zhe. "The Lipschitz ergodicity and generalized ergodicity of semigroups." SCIENTIA SINICA Mathematica 47, no. 1 (November 14, 2016): 205–20. http://dx.doi.org/10.1360/n012016-00090.

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29

Adams, Terrence M., and Cesar E. Silva. "Weak rational ergodicity does not imply rational ergodicity." Israel Journal of Mathematics 214, no. 1 (July 2016): 491–506. http://dx.doi.org/10.1007/s11856-016-1371-0.

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30

Lešanovský, Antonín. "Coefficients of ergodicity generated by non-symmetrical vector norms." Czechoslovak Mathematical Journal 40, no. 2 (1990): 284–94. http://dx.doi.org/10.21136/cmj.1990.102380.

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31

Veselý, Petr. "Two contributions to the theory of coefficients of ergodicity." Czechoslovak Mathematical Journal 42, no. 1 (1992): 73–88. http://dx.doi.org/10.21136/cmj.1992.128308.

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32

Zhang, Yu-Hui. "Strong ergodicity for single-birth processes." Journal of Applied Probability 38, no. 1 (March 2001): 270–77. http://dx.doi.org/10.1239/jap/996986662.

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An explicit and computable criterion for strong ergodicity of single-birth processes is presented. As an application, some sufficient conditions are obtained for strong ergodicity of an extended class of continuous-time branching processes and multi-dimensional Q-processes by comparison methods respectively. Consequently strong ergodicity of the Q-process corresponding to the finite-dimensional Schlögl model is proven.

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33

Spieksma, F. M. "Geometric Ergodicity of the ALOHA-system and a Coupled Processors Model." Probability in the Engineering and Informational Sciences 5, no. 1 (January 1991): 15–42. http://dx.doi.org/10.1017/s0269964800001868.

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μ-Geometric ergodicity of two-dimensional versions of the ALOHA and coupled processors models is verified by checking μ-geometric recurrence. Ergodicity and convergence of the Laplace-Stieltjes transforms in a neighborhood of 0 are necessary and sufficient conditions for the first model. The second model is exponential, for which ergodicity suffices to establish the required results.

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34

Zhang, Yu-Hui. "Strong ergodicity for single-birth processes." Journal of Applied Probability 38, no. 01 (March 2001): 270–77. http://dx.doi.org/10.1017/s0021900200018696.

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An explicit and computable criterion for strong ergodicity of single-birth processes is presented. As an application, some sufficient conditions are obtained for strong ergodicity of an extended class of continuous-time branching processes and multi-dimensional Q-processes by comparison methods respectively. Consequently strong ergodicity of the Q-process corresponding to the finite-dimensional Schlögl model is proven.

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35

SON, YOUNGHWAN. "Joint ergodicity of actions of an abelian group." Ergodic Theory and Dynamical Systems 34, no. 4 (March 8, 2013): 1353–64. http://dx.doi.org/10.1017/etds.2012.190.

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AbstractLet $G$ be a countable abelian group and let ${T}^{(1)} , {T}^{(2)} , \ldots , {T}^{(s)} $ be measure preserving $G$-actions on a probability space. We prove that joint ergodicity of ${T}^{(1)} , {T}^{(2)} , \ldots , {T}^{(s)} $ implies total joint ergodicity if each ${T}^{(i)} $ is totally ergodic. We also show that if $G= { \mathbb{Z} }^{d} $, $s\geq d+ 1$ and the actions ${T}^{(1)} , {T}^{(2)} , \ldots , {T}^{(s)} $ commute, then total joint ergodicity of ${T}^{(1)} , {T}^{(2)} , \ldots , {T}^{(s)} $ follows from joint ergodicity. This can be seen as a generalization of Berend’s result for commuting $ \mathbb{Z} $-actions.

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36

Poitras, Geoffrey, and John Heaney. "Classical Ergodicity and Modern Portfolio Theory." Chinese Journal of Mathematics 2015 (August 2, 2015): 1–17. http://dx.doi.org/10.1155/2015/737905.

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What role have theoretical methods initially developed in mathematics and physics played in the progress of financial economics? What is the relationship between financial economics and econophysics? What is the relevance of the “classical ergodicity hypothesis” to modern portfolio theory? This paper addresses these questions by reviewing the etymology and history of the classical ergodicity hypothesis in 19th century statistical mechanics. An explanation of classical ergodicity is provided that establishes a connection to the fundamental empirical problem of using nonexperimental data to verify theoretical propositions in modern portfolio theory. The role of the ergodicity assumption in the ex post/ex ante quandary confronting modern portfolio theory is also examined.

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37

Wang, Jian. "On the Exponential Ergodicity of Lévy-Driven Ornstein–Uhlenbeck Processes." Journal of Applied Probability 49, no. 4 (December 2012): 990–1004. http://dx.doi.org/10.1239/jap/1354716653.

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38

Wang, Jian. "On the Exponential Ergodicity of Lévy-Driven Ornstein–Uhlenbeck Processes." Journal of Applied Probability 49, no. 04 (December 2012): 990–1004. http://dx.doi.org/10.1017/s0021900200012833.

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39

Meitz, Mika, and Pentti Saikkonen. "Subgeometric ergodicity and β-mixing." Journal of Applied Probability 58, no. 3 (September 2021): 594–608. http://dx.doi.org/10.1017/jpr.2020.108.

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AbstractIt is well known that stationary geometrically ergodic Markov chains are $\beta$ -mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies $\beta$ -mixing under suitable moment assumptions. In this note we show that similar results hold also for subgeometrically ergodic Markov chains. In particular, for both stationary and other initial distributions, subgeometric ergodicity implies $\beta$ -mixing with subgeometrically decaying mixing coefficients. Although this result is simple, it should prove very useful in obtaining rates of mixing in situations where geometric ergodicity cannot be established. To illustrate our results we derive new subgeometric ergodicity and $\beta$ -mixing results for the self-exciting threshold autoregressive model.

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40

Zeifman, A. I. "Quasi-ergodicity for non-homogeneous continuous-time Markov chains." Journal of Applied Probability 26, no. 3 (September 1989): 643–48. http://dx.doi.org/10.2307/3214422.

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We consider a non-homogeneous continuous-time Markov chain X(t) with countable state space. Definitions of uniform and strong quasi-ergodicity are introduced. The forward Kolmogorov system for X(t) is considered as a differential equation in the space of sequences l1. Sufficient conditions for uniform quasi-ergodicity are deduced from this equation. We consider conditions of uniform and strong ergodicity in the case of proportional intensities.

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41

Zeifman, A. I. "Quasi-ergodicity for non-homogeneous continuous-time Markov chains." Journal of Applied Probability 26, no. 03 (September 1989): 643–48. http://dx.doi.org/10.1017/s0021900200038249.

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We consider a non-homogeneous continuous-time Markov chain X(t) with countable state space. Definitions of uniform and strong quasi-ergodicity are introduced. The forward Kolmogorov system for X(t) is considered as a differential equation in the space of sequences l 1 . Sufficient conditions for uniform quasi-ergodicity are deduced from this equation. We consider conditions of uniform and strong ergodicity in the case of proportional intensities.

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42

Perov, Anatoly Ivanovich. "KOLMOGOROV MATRIX, AND A CONTINUOUS MARKOV CHAIN WITH A FINITE NUMBER OF STATES." Tambov University Reports. Series: Natural and Technical Sciences, no. 123 (2018): 503–9. http://dx.doi.org/10.20310/1810-0198-2018-23-123-503-509.

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In terms of ergodicity of averaged systems with constant coefficients (and Kolmogorov matrix), the signs of ergodicity of continuous Markov chains with a finite number of States with periodic and almost periodic coefficients are indicated.

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43

Englman, Robert. "Ergodic Tendencies in Sub-Systems Coupled to Finite Reservoirs—Classical and Quantal." Symmetry 12, no. 10 (October 6, 2020): 1642. http://dx.doi.org/10.3390/sym12101642.

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Whereas ergodic theories relate to limiting cases of infinite thermal reservoirs and infinitely long times, some ergodicity tendencies may appear also for finite reservoirs and time durations. These tendencies are here explored and found to exist, but only for extremely long times and very soft ergodic criteria. “Weak ergodicity breaking” is obviated by a judicious time-weighting, as found in a previous work [Found. Phys. (2015) 45: 673–690]. The treatment is based on an N-oscillator (classical) and an N-spin (quantal) model. The showing of ergodicity is facilitated by pictorial presentations.

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44

Bunke, Ulrich, Stephane Nonnenmacher, and Roman Schubert. "Arbeitsgemeinschaft: Quantum Ergodicity." Oberwolfach Reports 8, no. 4 (2011): 2781–835. http://dx.doi.org/10.4171/owr/2011/49.

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45

Donnelly, Harold. "Quantum unique ergodicity." Proceedings of the American Mathematical Society 131, no. 9 (December 30, 2002): 2945–51. http://dx.doi.org/10.1090/s0002-9939-02-06810-7.

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46

Kaplan, L., and E. J. Heller. "Weak quantum ergodicity." Physica D: Nonlinear Phenomena 121, no. 1-2 (October 1998): 1–18. http://dx.doi.org/10.1016/s0167-2789(98)00156-0.

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47

Mauro, John C., Prabhat K. Gupta, and Roger J. Loucks. "Continuously broken ergodicity." Journal of Chemical Physics 126, no. 18 (May 14, 2007): 184511. http://dx.doi.org/10.1063/1.2731774.

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48

Pugh, Charles, Michael Shub, and Alexander Starkov. "Unique ergodicity, stable ergodicity, and the Mautner phenomenon for diffeomorphisms." Discrete & Continuous Dynamical Systems - A 14, no. 4 (2006): 845–55. http://dx.doi.org/10.3934/dcds.2006.14.845.

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49

Zheng, ZuoHuan. "Necessary and sufficient conditions for Lipschitz ergodicity and generalized ergodicity." Science China Mathematics 56, no. 4 (November 8, 2012): 777–87. http://dx.doi.org/10.1007/s11425-012-4489-5.

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50

Zhang, Yuhui. "Criteria on ergodicity and strong ergodicity of single death processes." Frontiers of Mathematics in China 13, no. 5 (September 28, 2018): 1215–43. http://dx.doi.org/10.1007/s11464-018-0722-z.

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