So, today we started a new topic: that of non stationary point processes. In particular, we looked at inhomogeneous Poisson processes and Cox processes. The former are Poisson processes where the rate change in time, in a deterministic manner. The latter are the same, only the rate is itself a stochastic process.
As usual, the lecture is here.
Inhomogeneous Poisson processes can be seen also from another point of view: instead of thinking of a process with changing rate. one can think of a standard Poisson process with intensity 1, where the time is distorted. The distortion is, of course, proportional to the rate.
The advantage of thinking that way is to define non stationary renewal process: a method is, in fact, to define a stationary process and then to operate a time distortion, which leads to a non stationary process.
And this is exactly what we will do next time.