January 29th, 2018, 5:53 pm
Well, I think the second equality in (1.22) can be "justified" by picturing a sample chart of [$]\pi(s)[$] vs. s. So, formally [$]d \pi(s) = \delta(s - t_i) \, ds[$]
in the vicinity of each [$]t_i[$], using Dirac deltas. Now integrate.
Then [$]d \pi^Y(s) = Y_i \,\delta(s - t_i) \, ds[$] in the same vicinity for the same reason, which was the other question.
Is it just notation? Probably. In general, jump-process notation is pretty awful and you just get used to it. (Should be in Student forum).