Branching processes form one of the classical fields of applied
probability and are still an active area of research. The field has by
now grown so large and diverse that a complete and unified treat- ment
is hardly possible anymore, let alone in one volume. So, our aim here
has been to single out some of the more recent developments and to
present them with sufficient background material to obtain a largely
self-contained treatment intended to supplement previous mo- nographs
rather than to overlap them. The body of the text is divided into four
parts, each of its own flavor. Part A is a short introduction, stressing
examples and applications. In Part B we give a self-contained and
up-to-date pre- sentation of the classical limit theory of simple
branching processes, viz. the Gal ton-Watson ( Bienayme-G-W) process and
i ts continuous time analogue. Part C deals with the limit theory of
Il!arkov branching processes with a general set of types under
conditions tailored to (multigroup) branching diffusions on bounded
domains, a setting which also covers the ordinary multitype case.
Whereas the point of view in Parts A and B is quite pedagogical, the aim
of Part C is to treat a large subfield to the highest degree of
generality and completeness possi"ble. Thus the exposition there is at
times quite technical.