%0 Journal Article %1 Duquesne:November2007:0178-8051:313 %A Duquesne, Thomas %A Winkel, Matthias %D November 2007 %J Probability Theory and Related Fields %K Levy_processes branching_processes %P 313-371(59) %R doi:10.1007/s00440-007-0064-3 %T Growth of Levy trees %U http://www.ingentaconnect.com/content/klu/440/2007/00000139/F0020003/00000064 %V 139 %X We construct random locally compact real trees called Lvy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton-Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Lvy tree as the limit of this growing family with respect to the Gromov-Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Lvy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure.

@article{Duquesne:November2007:0178-8051:313, abstract = {We construct random locally compact real trees called Lvy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton-Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Lvy tree as the limit of this growing family with respect to the Gromov-Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Lvy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure.}, added-at = {2008-07-10T23:00:46.000+0200}, author = {Duquesne, Thomas and Winkel, Matthias}, biburl = {https://www.bibsonomy.org/bibtex/29d1601dc09132efb7162e71ea017d16b/peter.ralph}, description = {Growth of Levy trees}, doi = {doi:10.1007/s00440-007-0064-3}, interhash = {8bd4bb50d7255c9f1605d6cfe615a8b9}, intrahash = {9d1601dc09132efb7162e71ea017d16b}, journal = {Probability Theory and Related Fields}, keywords = {Levy_processes branching_processes}, pages = {313-371(59)}, timestamp = {2008-07-10T23:00:46.000+0200}, title = {Growth of Levy trees}, url = {http://www.ingentaconnect.com/content/klu/440/2007/00000139/F0020003/00000064}, volume = 139, year = {November 2007} }