K. Breitung, W.-D. Richter
A geometric approach to an asymptotic expansion for large deviation probabilities of Gaussian Random Vectors
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.), See also {30E15}

41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)

Abstract: For the probabilities of large deviations of Gaussian random vectors
an asymptotic expansion is derived. Based upon a geometric measure
representation for the Gaussian law the interactions between global
and local geometric properties both of the distribution and of the
large deviation domain are studied. The advantage of the result is
that the expansion coefficients can be obtained by making a series
expansion of a surface integral avoiding the calculation of higher
order derivatives.

Keywords: Asymptotic expansions, Gaussian distribution, local geometric properties, geometric representation, large deviations, normal distribution, Watson's lemma