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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Spatial Branching Processes, Random Snakes and Partial Differential Equations (Paperback, 1999 ed.)
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Spatial Branching Processes, Random Snakes and Partial Differential Equations (Paperback, 1999 ed.)
Series: Lectures in Mathematics. ETH Zurich
Expected to ship within 10 - 15 working days
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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 in several limit theorems for
models of statistical mechanics. 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.
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