On stochastic setting of stationary phase method

A probability model _∫Rexp(ιnP(x)])dΦ_n(x) with Φ_n(x) the distribution function of random variable (ξ_k 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.