Probabilistic degenerate r-Stirling numbers of the second and probabilistic degenerate r-Bell polynomials

Abstract: Assume that Y is a random variable whose moment generating function exists in a neighborhood of the origin. We study the probabilistic degenerate r-Stirling numbers of the second kind associated with Y and the probabilistic degenerate r-Bell polynomials associated with Y. They are respectively probabilistic extensions of the degenerate r-Stirling numbers of the second and the degenerate r-Bell polynomials which are studied earlier. The aim of this paper is to obtain their properties, explicit expressions and related identities by means of generating functions.