Spatial Branching Processes, Random Snakes and Partial Differential Equations (Lectures in Mathematics. ETH Zürich) Book

This book introduces several remarkable new probabilistic objects that combine spatial motion with a continuous branching phenomenon and are closely related to certain semilinear partial differential equations. The Brownian snake approach is used to give a concrete and powerful presentation of superprocesses and also to investigate connections between superprocesses and partial differential equations. These are notable because almost every important probabilistic question corresponds to a significant analytic problem. This book is intended for postgraduate students and researchers in probability theory. It will also be of interest to mathematical physicists or specialists of PDE who want to learn about probabilistic methods. No prerequisites are assumed except for some familiarity with Brownian motion and the basic facts of the theory of stochastic processes. Although the text includes no new results, simplified versions of existing proofs are provided in several instances. Series: Lectures in MathematicsRead More