Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 35 / 6 / 2 / Solution

In the no-simultaneous-event infinitesimal representation, the event increment is binary, so $d{N}_{+}(t{)}^2=d{N}_{+}(t)$. Its second moment equals its first moment:This uses the assumed binary increment. In an ordinary finite interval more than one event is possible, and the equality would not hold exactly; the no-ties counting-process calculation concerns the first-order infinitesimal terms.