I am looking for a books on continuous time markov chains. The books should include:
-Conditions and proofs of what is necessary for there to be a finite number of transitions in every interval.
-The formula and its proof for the expected number of transitions from a given state to another in an interval.
-And also the formula for the expected value of $$\int_0^T f(t)dN_{ij}(t,\omega)$$, where f is an integrable function and and $dN_{ij}(t,\omega)$ is 1 if we have a jump from $i$ to $j$ at time t and zero if not.
Do you know about any books that will cover these topics? It doesn't have to be in only one book.