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The aim of this paper is to study probabilistic versions of the degenerateWhitney numbers of the second kind and those of the degenerate Dowlingpolynomials, namely the probabilistic degenerate Whitney numbers of the secondkind associated with Y and the probabilistic degenerate Dowling polynomialsassociated with Y. Here Y is a random variable whose moment generating functionexists in some neighborhood of the origin. We derive some properties, explicitexpressions, certain identities, recurrence relations and generating functionsfor those numbers and polynomials. In addition, we investigate theirgeneralizations, namely the probabilistic degenerate r-Whitney numbers of thesecond kind associated with Y and the probabilistic degenerate r-Dowlingpolynomials associated with Y, and get similar results to the aforementionednumbers and polynomials.

Probabilistic degenerate Dowling polynomials associated with random variables