Snakes and Spiders

We consider di usion processes on a class of R trees. The processes are de ned in a manner similar to that of Le Gall's Brownian snake. Each point in the tree has a real valued height" or generation", and the height of the di usion process evolves as a Brownian motion. When the height process decreases the di usion retreats back along a lineage, whereas when the height process increases the di usion chooses among branching lineages according to relative weights given by a possibly in nite measure on the family of lineages. The class of R trees we consider can have branch points with countably in nite branching and lineages along which the branch points have points of accumulation. We give a rigorous construction of the di usion process, identify its Dirichlet form, and obtain a necessary and su cient condition for it to be transient. We show that the tail eld of the di usion is always trivial and draw the usual conclusion that bounded space time harmonic functions are co...

• Type: Conference
• Year: 2000
• Where: ICPR
• Authors: Brendan McCane
• Keywords: Computer Vision, Di Usion, Di Usion Process, Di Usion Processes, ICPR 2000