%0 Book Section %1 csp-bf %A Pitman, Jim %B Combinatorial Stochastic Processes %D 2006 %I Springer-Verlag %K Brownian_motion Brownian_tree Dept_Mathematics_Berkeley Dept_Statistics_Berkeley random_trees_and_forests myown %P 143--175 %T The Brownian forest %U http://dx.doi.org/10.1007/3-540-34266-4_8 %V 1875 %X The Harris correspondence between random walks and random trees, reviewed in Section 6.3, suggests that a continuous path be regarded as encoding some kind of infinite tree, with each upward excursion of the path corresponding to a subtree. Thisidea has been developed and applied in various ways by Neveu- Pitman 324, 323, Aldous 5, 6, 7 and Le Gall 271, 272, 273,275. This chapter reviews this circle of ideas, with emphasis on how the Brownian forest can be grown to explore finer andfiner oscillations of the Brownian path, and how this forest growth process is related to Williams’ path decompositions ofBrownian motion at the time of a maximum or minimum. %& 8

@inbook{csp-bf, abstract = {The Harris correspondence between random walks and random trees, reviewed in Section 6.3, suggests that a continuous path be regarded as encoding some kind of infinite tree, with each upward excursion of the path corresponding to a subtree. Thisidea has been developed and applied in various ways by Neveu- Pitman [324, 323], Aldous [5, 6, 7] and Le Gall [271, 272, 273,275]. This chapter reviews this circle of ideas, with emphasis on how the Brownian forest can be grown to explore finer andfiner oscillations of the Brownian path, and how this forest growth process is related to Williams’ path decompositions ofBrownian motion at the time of a maximum or minimum.}, added-at = {2008-01-21T00:32:22.000+0100}, author = {Pitman, Jim}, biburl = {https://www.bibsonomy.org/bibtex/2dfed181918160b5fa778378ae20528ea/pitman}, booktitle = {Combinatorial Stochastic Processes}, chapter = 8, description = {SpringerLink - Book Chapter}, interhash = {f76a082fefcbee19fdee2cd3cea14091}, intrahash = {dfed181918160b5fa778378ae20528ea}, keywords = {Brownian_motion Brownian_tree Dept_Mathematics_Berkeley Dept_Statistics_Berkeley random_trees_and_forests myown}, pages = {143--175}, publisher = {Springer-Verlag}, series = {Lecture Notes in Mathematics}, timestamp = {2010-10-30T22:51:59.000+0200}, title = {The Brownian forest}, url = {http://dx.doi.org/10.1007/3-540-34266-4_8}, volume = 1875, year = 2006 }