
Lecture 16
Population dynamics
Let us first introduce the main components of our story and agree on
some notation.
The sequence
{β
i
}
∞
i=1
denotes the times of birth for individuals with given proper-
ties/characteristics: for example, individuals with the same place of
birth, belonging to a given socio-economic group, of the same eth-
nicity, etc. For us, the sequence of times of birth is just an increasing
sequence of random variables
0 < β
1
< β
2
< ··· .
Choosing the initial moment of 0 is a matter of agreement: it could
be the moment of Adam’s creation; or it could be the year 1900, for
which β
1
is the moment of the first birth on or after the 1st of January ...