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

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  • 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
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    References listed on IDEAS

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    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.
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