Stein's Method and Birth-Death Processes

By T. C. Brown, Aihua Xia. 2001

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A new metric between distributions of point processes (2007, result): “Numerous useful upper bounds in this metric have been obtained, including the results of [3], [6], [9], [11], [12], [22], and [23], which for the most part assume that one of the probability measures involved is a Poisson (or compound Poisson) process distribution.”
Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry (2014, unknown): “tion), one often uses weaker notions of distance. Starting with the work of Barbour and Brown [4] and 2 Barbour, Holst and Janson [8], this has been done by Brown, Chen, Schuhmacher, Weinberg and Xia [11, 12, 13, 15, 39, 40, 42]. Our work goes in the opposite direction since the KantorovichRubinstei”
Stein's method for steady-state diffusion approximations: an introduction through the Erlang-A and Erlang-C models (2015, methodology): “For examples of coupling arguments, see [5, 3, 11, 4, 23].”
Stein’s method, Palm theory and Poisson process approximation (2004, background): “As the arguments in Barbour and Brown (1992) and Brown and Xia (2001) never rely on the property that ρ0(x, y) = 0 implies x= y, the results are still valid for ρ0 and the pseudometrics ρ1 and ρ2 generated from ρ0.”