I was reading these math notes on Continuous Time Markov Chains and came across the following statements:
I have been trying to understand how the time-dependent Probability Transition Matrix can be related to the Convolution Integral. I have been trying to learn more about the Convolution Integral (e.g. https://tutorial.math.lamar.edu/classes/de/convolutionintegrals.aspx) - although I see a Convolution Integral occurring in the above equations - I am still not sure why pij(t0,t) can be written in the following way.
Can someone please help me understand the derivations of these two equations?
Thanks!