IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v16y2003i3d10.1023_a1025624600545.html

On Large Deviation Convergence of Invariant Measures

Author

Listed:
  • Anatolii A. Puhalskii

    (University of Colorado at Denver, Campus Box 170
    Institute for Problems in Information Transmission)

Abstract

We present new results on the connection between large deviation principles for trajectories of stochastic processes and the associated invariant measures. Applications to diffusion and queuing processes are provided.

Suggested Citation

  • Anatolii A. Puhalskii, 2003. "On Large Deviation Convergence of Invariant Measures," Journal of Theoretical Probability, Springer, vol. 16(3), pages 689-724, July.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:3:d:10.1023_a:1025624600545
    DOI: 10.1023/A:1025624600545
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1025624600545
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1025624600545?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Veretennikov, A. Yu., 1997. "On polynomial mixing bounds for stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 115-127, October.
    2. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
    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. Stilian A. Stoev & Murad S. Taqqu, 2007. "Limit Theorems for Sums of Heavy-tailed Variables with Random Dependent Weights," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 55-87, March.
    2. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.
    3. Saulius Minkevičius & Igor Katin & Joana Katina & Irina Vinogradova-Zinkevič, 2021. "On Little’s Formula in Multiphase Queues," Mathematics, MDPI, vol. 9(18), pages 1-15, September.
    4. Yuji Sakamoto & Nakahiro Yoshida, 2009. "Third-order asymptotic expansion of M-estimators for diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 629-661, September.
    5. Guillin, A. & Liptser, R., 2005. "MDP for integral functionals of fast and slow processes with averaging," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1187-1207, July.
    6. Cayé, Thomas & Herdegen, Martin & Muhle-Karbe, Johannes, 2020. "Scaling limits of processes with fast nonlinear mean reversion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1994-2031.
    7. Anatolii A. Puhalskii & Michael Jay Stutzer, 2016. "On minimising a portfolio's shortfall probability," Papers 1602.02192, arXiv.org, revised May 2017.
    8. Alexander Veretennikov, 2023. "Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited," Mathematics, MDPI, vol. 11(14), pages 1-16, July.
    9. Zhang, Tonglin, 2024. "Variables selection using L0 penalty," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    10. Basrak, Bojan & Špoljarić, Drago, 2015. "Extremes of random variables observed in renewal times," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 216-221.
    11. Bal'azs Gerencs'er & Mikl'os R'asonyi, 2020. "Invariant measures for multidimensional fractional stochastic volatility models," Papers 2002.04832, arXiv.org, revised Aug 2021.
    12. Kulik, Alexei & Pavlyukevich, Ilya, 2021. "Moment bounds for dissipative semimartingales with heavy jumps," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 274-308.
    13. Foucart, Clément & Yuan, Linglong, 2025. "Weak convergence of continuous-state branching processes with large immigration," Stochastic Processes and their Applications, Elsevier, vol. 179(C).
    14. Cassandra Milbradt & Dorte Kreher, 2022. "A cross-border market model with limited transmission capacities," Papers 2207.01939, arXiv.org, revised Nov 2024.
    15. Cetemen, Doruk & Hwang, Ilwoo & Kaya, Ayça, 2020. "Uncertainty-driven cooperation," Theoretical Economics, Econometric Society, vol. 15(3), July.
    16. Masayuki Uchida & Nakahiro Yoshida, 2001. "Information Criteria in Model Selection for Mixing Processes," Statistical Inference for Stochastic Processes, Springer, vol. 4(1), pages 73-98, January.
    17. Kanaya, Shin, 2017. "Convergence Rates Of Sums Of Α-Mixing Triangular Arrays: With An Application To Nonparametric Drift Function Estimation Of Continuous-Time Processes," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1121-1153, October.
    18. Stefan Ankirchner & Christophette Blanchet-Scalliet & Nabil Kazi-Tani, 2019. "The De Vylder-Goovaerts conjecture holds true within the diffusion limit," Post-Print hal-01887402, HAL.
    19. Penrose, Mathew D., 2000. "Central limit theorems for k-nearest neighbour distances," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 295-320, February.
    20. Lukas Gonon & Johannes Muhle‐Karbe & Xiaofei Shi, 2021. "Asset pricing with general transaction costs: Theory and numerics," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 595-648, April.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:jotpro:v:16:y:2003:i:3:d:10.1023_a:1025624600545. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.