Probabilistic fully degenerate Dowling polynomials associated with random variables

Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. The aim of this paper is to study the probabilistic degenerate Whitney numbers of the second kind associated with Y and the probabilistic fully degenerate Dowling polynomials associated with Y, which are the probabilistic versions of the degenerate Whitney numbers of the second kind and the fully degenerate Dowling polynomials. We derive generating functions, some properties, explicit expressions, certain identities, recurrence relations for those numbers and polynomials.