Metric entropy and the small deviation problem for stable processes

• Autorzy: Aurzada F.
• Języki publikacji: EN

Abstrakty

EN

The famous connection between metric entropy and small deviation probabilities of Gaussian processes was discovered by Kuelbs and Li in [6] and completed by Li and Linde in [9]. The question whether similar connections exist for other types of processes has remained open ever since. In [10], Li and Linde propose a first approach to this problem for stable processes. The present article clarifies the question completely for symmetric stable processes.

Słowa kluczowe

EN

small deviation; lower tail probability; Gaussian processes; stable processes; metric entropy

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2007
• Tom: Vol. 27, Fasc. 2
• Strony: 261--274
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Aurzada F.

• Technische Universität Berlin, Institut für Mathematik, Sekr. MA 7-5, Straße des 17. Juni 136, 10623 Berlin, Germany

Bibliografia

• [1] S. Artstein, Y. Milman and S. J. Szarek, Duality of metric entropy, Ann. of Math. (2) 159 (2004), pp. 1313-1328.
• [2] F. Aurzada, On the lower tail probabilities of some random sequences in lp, preprint (2005), to appear in: J. Theoret. Probab., available at: http://www.springerlink.com/content/ 2487424381403th0/?p = 018780b6b8e34648916c47dc98cc8601&pi = 0
• [3] F. Aurzada, Small deviations for stable processes via compactness properties of the parameter set, preprint (2006), to appear in: Statist. Probab. Lett., available at: http://www.math.tu-ber- lin.de/ ~ aurzada/sdviadudleymetric.pdf
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• [8] M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, Berlin 1991.
• [9] W. Y. Li and W. Linde, Approximation, metric entropy and small ball estimates for Gaussian measures, Ann. Probab. 27 (1999), pp. 1556-1578.
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• [14] G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes, Chapman and Hall, New York 1994.
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