Probabilistic bivariate Bell polynomials

Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. We consider the probabilistic bivariate Bell polynomials associated with Y and the probabilistic bivariate r-Bell polynomials associated with Y. For those polynomials, we derive the recurrence relations corresponding to the ones found by Zheng and Li for the bivariate Bell polynomials and the bivariate r-Bell polynomials.