Home > Authors > Jean-Francois Le Gall > Spatial Branching Processes, Random Snakes and Partial Differential Equations (Lectures in Mathematics. ETH Zürich)
Spatial Branching Processes, Random Snakes and Partial Differential Equations (Lectures in Mathematics. ETH Zürich)
The text includes a presentation of the measure-valued branching processes also called superprocesses and of their basic properties. In the important quadratic branching case, the path-valued process known as the Brownian snake is used to give a concrete and powerful representation of superprocesses. This representation is applied to several connections with a class of semilinear partial differential equations. On the one hand, these connections give insight into properties of superprocesses. On the other hand, the probabilistic point of view sometimes leads to new analytic results, concerning for instance the trace classification of positive solutions in a smooth domain. An important tool is the analysis of random trees coded by linear Brownian motion. This includes the so-called continuum random tree and leads to the fractal random measure known as ISE, which has appeared recently...
See on goodreads | librarything
