IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v227y2026ics016771522500166x.html

Strong law of large numbers for random walks in weakly dependent random scenery

Author

Listed:
  • Sharipov, Sadillo

Abstract

In this brief note, we study the strong law of large numbers for random walks in random scenery. Under the assumptions that the random scenery is non-stationary and satisfies weakly dependent condition with an appropriate rate, we establish strong law of large numbers for random walks in random scenery. Our results extend the known results in the literature.

Suggested Citation

  • Sharipov, Sadillo, 2026. "Strong law of large numbers for random walks in weakly dependent random scenery," Statistics & Probability Letters, Elsevier, vol. 227(C).
    • Handle: RePEc:eee:stapro:v:227:y:2026:i:c:s016771522500166x
    DOI: 10.1016/j.spl.2025.110521
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771522500166X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2025.110521?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. N. Guillotin-Plantard, 2001. "Dynamic ℤ d -Random Walks in a Random Scenery: A Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 14(1), pages 241-260, January.
    2. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    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. Jerôme Dedecker & Paul Doukhan, 2002. "A New Covariance Inequality and Applications," Working Papers 2002-25, Center for Research in Economics and Statistics.
    2. Hwang, Eunju & Shin, Dong Wan, 2014. "Infinite-order, long-memory heterogeneous autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 339-358.
    3. Guessoum, Zohra & Ould Saïd, Elias & Sadki, Ourida & Tatachak, Abdelkader, 2012. "A note on the Lynden-Bell estimator under association," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1994-2000.
    4. Yuan, Zihao & Spindler, Martin, 2025. "Bernstein-type inequalities and nonparametric estimation under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 251(C).
    5. Carvalho, Carlos & Masini, Ricardo & Medeiros, Marcelo C., 2018. "ArCo: An artificial counterfactual approach for high-dimensional panel time-series data," Journal of Econometrics, Elsevier, vol. 207(2), pages 352-380.
    6. Hwang, Eunju & Shin, Dong Wan, 2012. "Strong consistency of the stationary bootstrap under ψ-weak dependence," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 488-495.
    7. Eunju Hwang & Dong Shin, 2016. "Kernel estimators of mode under $$\psi $$ ψ -weak dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 301-327, April.
    8. Kojevnikov, Denis & Marmer, Vadim & Song, Kyungchul, 2021. "Limit theorems for network dependent random variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 882-908.
    9. Moysiadis, Theodoros & Fokianos, Konstantinos, 2014. "On binary and categorical time series models with feedback," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 209-228.
    10. Alain Durmus & Eric Moulines & Alexey Naumov & Sergey Samsonov, 2024. "Probability and Moment Inequalities for Additive Functionals of Geometrically Ergodic Markov Chains," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2184-2233, September.
    11. Dedecker, Jérôme & Prieur, Clémentine, 2007. "An empirical central limit theorem for dependent sequences," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 121-142, January.
    12. McElroy, Tucker & Politis, Dimitris N., 2013. "Distribution theory for the studentized mean for long, short, and negative memory time series," Journal of Econometrics, Elsevier, vol. 177(1), pages 60-74.
    13. Wu, Wei Biao & Huang, Yinxiao & Huang, Yibi, 2010. "Kernel estimation for time series: An asymptotic theory," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2412-2431, December.
    14. Sancetta, Alessio, 2008. "Sample covariance shrinkage for high dimensional dependent data," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 949-967, May.
    15. Pinkse, Joris & Shen, Lihong & Slade, Margaret, 2007. "A central limit theorem for endogenous locations and complex spatial interactions," Journal of Econometrics, Elsevier, vol. 140(1), pages 215-225, September.
    16. Mamadou Lamine Diop & William Kengne, 2023. "A general procedure for change-point detection in multivariate time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 1-33, March.
    17. Xuan Liang & Jiti Gao & Xiaodong Gong, 2022. "Semiparametric Spatial Autoregressive Panel Data Model with Fixed Effects and Time-Varying Coefficients," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1784-1802, October.
    18. Christis Katsouris, 2022. "Asymptotic Theory for Unit Root Moderate Deviations in Quantile Autoregressions and Predictive Regressions," Papers 2204.02073, arXiv.org, revised Aug 2023.
    19. Cui, Yunwei & Zheng, Qi, 2017. "Conditional maximum likelihood estimation for a class of observation-driven time series models for count data," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 193-201.
    20. Doukhan, P. & Pommeret, D. & Reboul, L., 2015. "Data driven smooth test of comparison for dependent sequences," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 147-165.

    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:eee:stapro:v:227:y:2026:i:c:s016771522500166x. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.