Hints: Doob decomposition of a partial sum

Eksempler: <a href="https://tma4275.math.ntnu.no/discrete-time-martingales/doob-decomposition-discrete-time/problem-doop-decomposition-partial-sum/hints-doob-decomposition-partial-sum/solution-doob-decomposition-partial-sum/">Solution: Doob decomposition of a partial sum
Videoer: <a class="video" href="https://ntnu.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=96d8f8ae-8cd5-4a46-a68d-af9600cba8e3">Doob decomposition (discrete time) (0:06:06, Håkon Tjelmeland)

Eksempel

Hints

The formula and explanation of the Doob decomposition is given in section 2.1.4 in ABG. Alternatively you can watch the video linked below. Remember that \(U_n\) is independent of \(\mathcal{F}_{n-1}\)!