I’m quite rusty, and this was never my field, but it isn’t immediately obvious why you get the…
Phyllis Little
1

So the transition operator in the continuous time case might be thought of as a matrix of differentials. Instead of s mapping to Ts, it instead maps to Tsdt. Then we can integrate over the time domain to get the total change.

I was actually a bit concerned about the notation I used, as it isn’t clear that the probability distribution/density is a function of time.