Moment-Free Kunchenko Stochastic Polynomials via Empirical Characteristic Function (opens in new tab)

We give a characteristic-function formulation of Kunchenko's stochastic-polynomial construction for settings in which raw moments may fail to exist. In the finite-variance trigonometric case, the coefficients of the Kunchenko normal system are expressed through the characteristic function and its derivative. In the moment-free case, empirical characteristic functions on a fixed finite frequency grid define a bounded discrepancy geometry that rem...