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.
Similar content being viewed by others
References
Bolthausen, E. A central limit theorem for two-dimensional random walks in random sceneries. Ann. Probab., 17:108–115 (1989)
Csáki, E., König, W., Shi, Z. An embedding for the Kesten-Spitzer random walk in random scenery. Stoch. Process. Appl., 82:283–292 (1999)
Kesten, H., Spitzer, F. A limit theorem related to a new class of self-similar process. Z. Wahrsch. verw. Gebiete, 50:5–25 (1979)
Khoshnevisan, D., Lewis, T.M. A law of the iterated logarithm for stable processes in random scenery. Stoch. Process. Appl., 74:89–121 (1998)
Lewis, T.M. A self normalized law of the iterated logarithm for random walk in random scenery. J. Theoret. Probab., 5:629–659 (1992)
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)
Petrov, V.V. Limit Theorem of Probability. Oxford Science Publications, Oxford, 1995
Taqqu, M.S. Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. verw. Gebiete, 31:287–302 (1975)
Wang, W. Weak convergence to fractional Brownian motion in Brownian motion. Probab. Th. Their Fields, 126:203–220 (2003)
Zhang, L.X. Strong approximation for the generalied Kesten-Spitzer random walk of independent scenery. Science in China, 31:230–241 (2001)
Zhang, L.X. The strong approximation for Kesten-Spitzer random walk. Statist. Probab. Lett., 53:21–26 (2001)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (No. 10401037) and Doctoral Program Foundation of the Ministry of Education of China (No. 20060269016).
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10255-007-0389-9