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- ItemA simple path to asymptotics for the frontier of a branching Brownian motion(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Roberts, Matthew I.We give proofs of two results about the position of the extremal particle in a branching Brownian motion, one concerning the median position and another the almost sure behaviour. Our methods are based on a many-to-two lemma which allows us to estimate the effect of the branching structure on the system by considering two dependent Bessel processes.
- ItemThe many-to-few lemma and multiple spines(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Harris, Simon S.; Roberts, Matthew I.We develop an extension to the spine theory of branching processes, and use it to give a simple and intuitive identity for calculating additive functionals of such processes, generalizing the well-known many-to-one lemma.