Stochastic Comparability and Dual Q-Functions

• Published in: Journal of mathematical analysis and applications Vol. 234; no. 2; pp. 482 - 499
• Main Authors: Zhang, Hanjun, Chen, Anyue
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 15.06.1999; Elsevier
• Subjects: duality; Exact sciences and technology; Feller–Reuter–Riley transition functions; Mathematics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; stochastic comparability; stochastic monotonicity; Stochastic processes; zero-entrance; zero-exit; zero-entrance; stochastic monotonicity; Feller–Reuter–Riley transition functions; stochastic comparability; duality; zero-exit; Markov chain; Feller Reuter Riley transition function; Stochastic monotonicity; Transition; Duality; Stochastic process; Stochastic comparability; Zero exit
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1006/jmaa.1999.6356

In this paper we discuss the relationship and characterization of stochastic comparability, duality, and Feller–Reuter–Riley transition functions which are closely linked with each other for continuous time Markov chains. A necessary and sufficient condition for two Feller minimal transition functions to be stochastically comparable is given in terms of their density q-matrices only. Moreover, a necessary and sufficient condition under which a transition function is a dual for some stochastically monotone q-function is given in terms of, again, its density q-matrix. Finally, for a class of q-matrices, the necessary and sufficient condition for a transition function to be a Feller–Reuter–Riley transition function is also given.