Intertwining and commutation relations for birth-death processes (Q2435226)

Using the intertwining relations for the M/M/1 and the M/M/\(\infty\) queues as a starting point, the authors obtain similar intertwining relations for more general birth-death processes. Under an additional assumption of convexity, they also derive sub-commutation relations for the birth-death processes. Applications of the main results are given to (a) Lipschitz contraction and Wasserstein curvature; (b) functional inequalities including Poincaré, entropic, isoperimetric and transportation-information inequalities; (c) hitting time of the origin for the M/M/1 queue, and (d) convex domination and stochastic orderings.