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Journal of Zhejiang University SCIENCE A 2002 Vol.3 No.5 P.579-583

http://doi.org/10.1631/jzus.2002.0579


Some limsup results for increments of stable processes in random scenery


Author(s):  HUANG Wei

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China

Corresponding email(s):   h_wei2002@163.com

Key Words:  Local time, Random walk in random scenery, Stable process in random scenery, Increments, Lag increments


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HUANG Wei. Some limsup results for increments of stable processes in random scenery[J]. Journal of Zhejiang University Science A, 2002, 3(5): 579-583.

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Abstract: 
In this paper, we prove some limsup results for increments and lag increments of G(t), which is a stable processe in random scenery. The proofs rely on the tail probability estimation of G(t).

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Reference

[1] Csaki, E., Konig, W., Shi, Z., 1999. An embedding for the Kesten-Spitzer random walk in random scenery. Stochast. Process. Appl., 82:283-292.

[2] Csorgo, M., Revesz, P., 1981. Strong Approximations in Probability and Statistics. Akademiai Kiado, Budapest, p.24-35.

[3] Kesten, H., Spitzer, F., 1979. A limit theorem related to a new class of self-similar processes. Z. Wahrsch. Verew. Gebitte., 50:5-25.

[4] Khoshnevisan, D., Lewis, T.M., 1998. A law of the iterated logarithm for stable processes in random scenery. Stochast. Process. Appl.,74:89-121.

[5] Lin, Z.Y., Lu, C.R., 1992. Strong Limit Theorems. Kluwer Publishing Co. & Science Press, China, p.10-14.

[6] Revesz, R.,1990. Random Walk in Random and Non-Random Environments. World Scientific, Singapore, p.310-312.

[7] Zhang L.X., 2001a. The strong approximation for the Kesten-Spitzer random walk. Statist. Probab. Lett., 53: 21-26.

[8] Zhang, L.X., 2001b. The strong approximation for the general Kesten-Spitzer random walk in independent random secenery. Science in China, 44A:619-630.

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