Probabilistic Central Bell Polynomials

Let [Formula: see text] be a random variable whose moment generating function exists in a neighborhood of the origin. The probabilistic central Bell polynomials associated with the random variable [Formula: see text] are investigated in this paper, as probabilistic extension of the central Bell polynomials. Furthermore, we consider the probabilistic central Fubini polynomials associated with [Formula: see text] and the probabilistic central factorial numbers of the second order associated with [Formula: see text]. The aim of this research is to obtain some characteristics, explicit expressions, specific identities, and recurrence relations for those numbers and polynomials.