IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/124582.html
   My bibliography  Save this paper

On metastability

Author

Listed:
  • Miclo, Laurent

Abstract

Consider finite state space irreducible and absorbing Markov processes. A general spectral criterion is provided for the absorbing time to be close to an exponential random variable, whatever the starting point. When exiting points are added to the state space, our criterion also insures that the exit time and position are almost independent. Since this is valid for any exiting extension of the state space, it corresponds to an instance of the metastability phenomenon. Simple examples at small temperature suggest that this new spectral criterion is quite sharp. But the main interest of the underlying quantitative approach, based on Poisson equations, is that it does not rely on a small parameter such as temperature, nor on reversibility.

Suggested Citation

  • Miclo, Laurent, 2020. "On metastability," TSE Working Papers 20-1128, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:124582
    as

    Download full text from publisher

    File URL: https://perso.math.univ-toulouse.fr/miclo/files/2020/07/metastability.pdf
    File Function: Full Text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    2. Elena-Corina Cipu, 2019. "Duality Results in Quasiinvex Variational Control Problems with Curvilinear Integral Functionals," Mathematics, MDPI, vol. 7(9), pages 1-9, September.
    3. Hanno Gottschalk & Marco Reese, 2021. "An Analytical Study in Multi-physics and Multi-criteria Shape Optimization," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 486-512, May.
    4. Karel Van Bockstal, 2020. "Existence of a Unique Weak Solution to a Nonlinear Non-Autonomous Time-Fractional Wave Equation (of Distributed-Order)," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    5. Savin Treanţă, 2019. "On Locally and Globally Optimal Solutions in Scalar Variational Control Problems," Mathematics, MDPI, vol. 7(9), pages 1-8, September.
    6. Darvishi, M.T. & Najafi, Mohammad & Wazwaz, Abdul-Majid, 2021. "Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    7. Ivan Francisco Yupanqui Tello & Alain Vande Wouwer & Daniel Coutinho, 2021. "A Concise Review of State Estimation Techniques for Partial Differential Equation Systems," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    8. Christian Klein & Julien Riton & Nikola Stoilov, 2021. "Multi-domain spectral approach for the Hilbert transform on the real line," Partial Differential Equations and Applications, Springer, vol. 2(3), pages 1-19, June.
    9. Marco Cirant & Roberto Gianni & Paola Mannucci, 2020. "Short-Time Existence for a General Backward–Forward Parabolic System Arising from Mean-Field Games," Dynamic Games and Applications, Springer, vol. 10(1), pages 100-119, March.
    10. Christian Kuehn & Cinzia Soresina, 2020. "Numerical continuation for a fast-reaction system and its cross-diffusion limit," Partial Differential Equations and Applications, Springer, vol. 1(2), pages 1-26, April.
    11. Zaiping Zhu & Andres Iglesias & Liqi Zhou & Lihua You & Jianjun Zhang, 2022. "PDE-Based 3D Surface Reconstruction from Multi-View 2D Images," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
    12. Wei Zhou & Xingxing Hao & Kaidi Wang & Zhenyang Zhang & Yongxiang Yu & Haonan Su & Kang Li & Xin Cao & Arjan Kuijper, 2020. "Improved estimation of motion blur parameters for restoration from a single image," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-21, September.
    13. Denny Ivanal Hakim & Yoshihiro Sawano, 2021. "Complex interpolation of variable Morrey spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 294(11), pages 2140-2150, November.
    14. Knut K. Aase & Petter Bjerksund, 2021. "The Optimal Spending Rate versus the Expected Real Return of a Sovereign Wealth Fund," JRFM, MDPI, vol. 14(9), pages 1-36, September.
    15. Frikha, Noufel & Li, Libo, 2021. "Well-posedness and approximation of some one-dimensional Lévy-driven non-linear SDEs," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 76-107.
    16. Tim Breitenbach & Alfio Borzì, 2020. "The Pontryagin maximum principle for solving Fokker–Planck optimal control problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 499-533, June.
    17. Li, Yixin & Hu, Xianliang, 2022. "Artificial neural network approximations of Cauchy inverse problem for linear PDEs," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    18. Yasunori Maekawa, 2021. "Note on smoothing estimates for Kolmogorov type equations," Partial Differential Equations and Applications, Springer, vol. 2(6), pages 1-12, December.
    19. Caroline Geiersbach & Teresa Scarinci, 2021. "Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 78(3), pages 705-740, April.
    20. Arturo Melián-González, 2021. "The Expenditure Rule in the Spanish Organic Law on Budgetary Stability and Financial Sustainability and its Impact on the Autonomous Communities," Hacienda Pública Española / Review of Public Economics, IEF, vol. 237(2), pages 57-84, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tse:wpaper:124582. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.