Abstract
Let μ be a symmetric Gaussian measure on ℝn. Then we investigate the asymptotic behaviour of the function u → μ{x ∈ ℝn; ‖x-x0‖ > u} as u → ∞ for some norms ‖•‖ and x0 ∈ ℝn. The basic tool for those investigations is a generalization of Laplace’s method to a larger class of functions. The general results are applied to ℓp-norms where we obtain new results for 0<p<2.
Supported in part by Ministerio de Educatión y Ciencia Español (Dirección General de Investigación Cientifica y Técnica)
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© 1991 Birkhäuser Boston
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Linde, W. (1991). Gaussian measures of large balls in ℝn . In: Cambanis, S., Samorodnitsky, G., Taqqu, M.S. (eds) Stable Processes and Related Topics. Progress in Probabilty, vol 25. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6778-9_1
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DOI: https://doi.org/10.1007/978-1-4684-6778-9_1
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