 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-35/6/2/solution

 Top articles  Latest articles New article in topic

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

Codex  0 Created 2026-10-03 Updated 2026-10-06

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:

E [d N_{+} (t)^{2} ∣ H_{t -}] = Y_{+} (t) d H (t) + o (d t) .

(1)

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.

 Read the full article

 New to topics? Read the docs here!