Asymptotic value of a multidimensional normal probability integral

摘要

Laplace's method of asymptotic estimation of integrals is extended to deal with multidimensional normal probability integrals. A multidimensional normal distribution is integrated over a region which does not include the origin, and an asymptotic value is obtained for small values of the variance. The method is illustrated by an error probability calculation in a communication system using M-level differential phase shift keying.