Height process for super-critical continuous state branching process

Abstract

We define the height process for super-critical continuous state branching processes with quadratic branching mechanism. It appears as a projective limit of Brownian motions with positive drift reflected at 0 and a>0 as a goes to infinity. Then we extend the pruning procedure of branching processes to the super-critical case. This give a complete duality picture between pruning and size proportional immigration for quadratic continuous state branching processes.

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• Snake representation of a superprocess in random environment
• Brownian continuum random tree conditioned to be large
• Approximation of the Height process of a CSBP with interaction