The aim of this monograph is to show how random sums (that is, the
summation of a random number of dependent random variables) may be
used to analyse the behaviour of branching stochastic processes.
The author shows how these techniques may yield insight and new
results when applied to a wide range of branching processes. In
particular, processes with reproduction-dependent and
non-stationary immigration may be analysed quite simply from this
perspective. On the other hand some new characterizations of the
branching process without immigration dealing with its genealogical
tree can be studied. Readers are assumed to have a firm grounding
in probability and stochastic processes, but otherwise this account
is self-contained. As a result, researchers and graduate students
tackling problems in this area will find this makes a useful
contribution to their work.
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