On stochastic setting of stationary phase method (Q550658)

The author considers a stochastic version of the so-called stationary phase method, which is a method to deal with oscillatory integrals and to find raw approximations of these. Instead of Lebesgue integrals expectations with respect to rescaled sums of i.i.d. variables are investigated. The approximating expectation is with respect to standard normal distribution. The author remarks that the methods are reminiscent to methods from the field of large deviation theory.