According to the definition,
for some number
and infinitesimal
.
The number
is called "intensity" of Poisson process.
In the applications of the following chapters we will be interested in the
time
of the first Poisson jump. We introduce the notation
for the filtration generated by the process
.
The following properties directly follow from the definitions:


(Poisson property 1)



(Poisson property 1a)

