44 citations · 119 across the 36 of their papers we have counts for
36 papers
Stein's method, Gaussian processes and Palm measures, with applications to queueing
A. D. Barbour, Nathan Ross, Guangqu Zheng
We develop a general approach to Stein's method for approximating a random process in the path space by a real continuous Gaussian process. We then use the approa…
Stein's method, smoothing and functional approximation
A. D. Barbour, Nathan Ross, Guangqu Zheng
Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals of a càdlàg random process of interest…
The expected degree distribution in transient duplication divergence models
A. D. Barbour, Tiffany Y. Y. Lo
We study the degree distribution of a randomly chosen vertex in a duplication--divergence graph, under a variety of different generalizations of the basic model of Bhan, Galas and…
Estimating the correlation in network disturbance models
A. D. Barbour, Gesine Reinert
The Network Disturbance Model of Doreian (1989) expresses the dependency between observations taken at the vertices of a network by modelling the correlation between neighbouring v…
Local limit theorems for occupancy models
A. D. Barbour, Peter Braunsteins, Nathan Ross
We present a rather general method for proving local limit theorems, with a good rate of convergence, for sums of dependent random variables. The method is applicable when a Stein…
Long-term concentration of measure and cut-off
Andrew Barbour, Graham Brightwell, Malwina Luczak
We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wasserstein distance. These are particularly suited…