Abstract
Throughout this paper \( (\xi_k)_{k=1}^{\infty} \) denotes a sequence of independent, centered, Gaussian random variables with variance one. We shall study the behavior of
as ε → 0+ for p > 0 where \( (a_{k})_{k=1}^{\infty} \) is a given sequence of positive numbers and \( \sum_{k\geq1}a_{k}< +\infty \).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cox, D.D. (1980). Normalized Brownian motion on Banach spaces. Ph.D. thesis, University of Washington, Seattle.
Cox, D.D. (1982). On the existence of natural rate of escape functions for infinite dimensional Brownian motions. Ann. Prob. 10, 623–638.
Erickson, K.B. (1980). Rates of escape of infinite dimensional Brownian motion. Ann. Prob. 8, 325–338.
Hoffmann-Jørgensen, J., Shepp, L.A. and Dudley, R.M. (1979). On the lower tail of Gaussian seminorms. Ann. Prob. 7, 319–342.
Kuelbs, J. (1978). Rates of growth for Banach space valued independent increments processes. Proc. of the 2nd Oberwolfach conference on probability on Banach spaces. Lecture Notes in Math. 709, Springer, Berlin, pp. 151–169.
Li, W.V. (1992). Comparison results for the lower tail of Gaussian seminorms. J. Theor. Probab. 5, 1–31.
Saint-Raymond, J. (1981). Sur le volume des corps convexes symetriques. Seminaire d’Initation a l’Analyse. Math. Univ. Pierre et Marie Curie, 46, Univ. Paris VI, Paris, Exp. No 11.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media New York
About this chapter
Cite this chapter
Li, W.V. (1992). On the Lower Tail of Gaussian Measures on l p . In: Dudley, R.M., Hahn, M.G., Kuelbs, J. (eds) Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference. Progress in Probability, vol 30. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0367-4_7
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0367-4_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6728-7
Online ISBN: 978-1-4612-0367-4
eBook Packages: Springer Book Archive