Special Topic: Bienaymé–Galton–Watson Simple Branching Process and Excursions

The tree contours and heights are identified as two natural discrete parameter stochastic processes associated with the branching process introduced in Chapter 14 as a probability distribution on a metric space of family trees. Analysis of contour paths in the special case of critical (shifted) geometric offspring distributions leads naturally to consideration of continuous parameter processes in terms of Brownian motion excursions.