1 citations · 1 across the 4 of their papers we have counts for
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Approximating inter-point distances in directed Bernoulli graphs
A. D. Barbour, Gesine Reinert
In directed random graphs, in which edges can be assigned to have one of two directions, or perhaps both, the distance between two vertices and can be computed along paths…
Convergence to equilibrium for density dependent Markov jump processes
Andrew Barbour, Graham Brightwell, Malwina Luczak
We investigate the convergence to (quasi--)equilibrium of a density dependent Markov chain in~, whose drift satisfies a system of ordinary differential equations hav…
Multivariate approximation in total variation, II: discrete normal approximation
A. D. Barbour, Malwina J. Luczak, Aihua Xia
The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in . We illustrate the use of the method f…
Multivariate approximation in total variation, I: equilibrium distributions of Markov jump processes
A. D. Barbour, Malwina J. Luczak, Aihua Xia
For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variation, in much the same way that the normal family i…
Central limit approximations for Markov population processes with countably many types
A. D. Barbour, M. J. Luczak
When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious n…