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Strong Laws of Large Numbers for Random Walks in Random Sceneries

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Abstract

In this paper, we study strong laws of large numbers for random walks in random sceneries. Some mild sufficient conditions for the validity of strong laws of large numbers are obtained.

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References

  1. Bolthausen, E. A central limit theorem for two-dimensional random walks in random sceneries. Ann. Probab., 17:108–115 (1989)

    MATH  MathSciNet  Google Scholar 

  2. Csáki, E., König, W., Shi, Z. An embedding for the Kesten-Spitzer random walk in random scenery. Stoch. Process. Appl., 82:283–292 (1999)

    Article  MATH  Google Scholar 

  3. Kesten, H., Spitzer, F. A limit theorem related to a new class of self-similar process. Z. Wahrsch. verw. Gebiete, 50:5–25 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  4. Khoshnevisan, D., Lewis, T.M. A law of the iterated logarithm for stable processes in random scenery. Stoch. Process. Appl., 74:89–121 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  5. Lewis, T.M. A self normalized law of the iterated logarithm for random walk in random scenery. J. Theoret. Probab., 5:629–659 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Lewis, T.M. A law of the iterated logarithm for random walk in random scenery with deterministic normalizers. J. Theoret. Probab., 6:209–230 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Petrov, V.V. Limit Theorem of Probability. Oxford Science Publications, Oxford, 1995

  8. Taqqu, M.S. Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. verw. Gebiete, 31:287–302 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  9. Wang, W. Weak convergence to fractional Brownian motion in Brownian motion. Probab. Th. Their Fields, 126:203–220 (2003)

    Article  MATH  Google Scholar 

  10. Zhang, L.X. Strong approximation for the generalied Kesten-Spitzer random walk of independent scenery. Science in China, 31:230–241 (2001)

    Google Scholar 

  11. Zhang, L.X. The strong approximation for Kesten-Spitzer random walk. Statist. Probab. Lett., 53:21–26 (2001)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Wen-sheng Wang.

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Supported by the National Natural Science Foundation of China (No. 10401037) and Doctoral Program Foundation of the Ministry of Education of China (No. 20060269016).

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Wang, Ws. Strong Laws of Large Numbers for Random Walks in Random Sceneries. Acta Mathematicae Applicatae Sinica, English Series 23, 495–500 (2007). https://doi.org/10.1007/s10255-007-0389-9

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  • DOI: https://doi.org/10.1007/s10255-007-0389-9

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