The Kolmogorov Equations
The Kolmogorov equations are used during to model birth and death processes.
Suppose the population at timeiswith probabilityso we can writeSuppose also that the probability that the population changes fromto in the time intervalis written
At timewe can write
If the birth rate when the population isis writtenand the death rate isthen
Substituting (2), (3) and (4) into (1) gives
These are the Kolmogorov forward equations.