Gaussian measures of large balls in ℝn

  • Werner Linde
Part of the Progress in Probabilty book series (PRPR, volume 25)


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.


Covariance Matrix Gaussian Process GAUSSIAN Measure Full Support Large Ball 
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Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • Werner Linde
    • 1
  1. 1.Friedrich-Schiller-Universität JenaJenaGerman Democratic Republic

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