Feynman diagrams and their limits for Bernoulli noise

Abstract

In this article, we will construct an approximation of Gaussian white noise based on the sequence of Bernoulli random variables and define Wick products and the stochastic exponent for the Bernoulli case. Here we will propose a method to calculate the expectations of Wick products for Bernoulli noise using diagrams, that converge to Feynman diagrams in the Gaussian case. We will prove that orthogonal polynomials for Bernoulli noise converge to Hermite polynomials, which form an orthogonal system in the Gaussian case.