  The Poisson process is the most elementary continuous-time stochastic process
that models a stream of repeating events. It is uniquely characterised by a
single parameter called the rate. Instead of a single value for this rate, we
here consider a rate interval and let it characterise two nested sets of
stochastic processes. We call these two sets of stochastic process imprecise
Poisson processes, explain why this is justified, and study the corresponding
lower and upper (conditional) expectations. Besides a general theoretical
framework, we also provide practical methods to compute lower and upper
(conditional) expectations of functions that depend on the number of events at
a single point in time.
