ON STOCHASTIC DOMINANCE OF NILPOTENT OPERATORS

In this paper, motivated by Nica and Speicher [Lectures on the Combinatorics of Free Probability, London Mathematical Society Lecture Note Series, Vol. 335 (Cambridge University Press, 2006)] and Kubo and Kuo [MRM-factors for the probability measures in the Meixner class, Infin. Dimens. Anal. Quantum Probab. Relat. Top.13 (2010) 525–550], we characterize a particular nilpotent case of a truncated forward shift operator by applying the technique of the random walks with repeated reflections and associated renewal equations. We also establish a stochastic order relationship by applying the crossing criteria.