On stochastic setting of stationary phase method

A probability model ∫Rexp(ι[nP(x)])dΦn(x) with Φn(x) the distribution function of random variable (ξk is i.i.d. sequence of r.v.’s with zero expectation and unit variance), being in a framework of stationary phase method is analyzed. The asymptotic expansion in CLT and Hörmander’s theorem play crucial role in asymptotic analysis of the model.