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Towards a general Doob-Meyer decomposition theorem

Jakubowski A.

Probability and Mathematical Statistics

2006

Vol. 26, Fasc. 1

143--153

Both the Doob-Меуег and Graversen-Rao decomposition theorems can be proved following an approach based on predictable compensators of discretizations and weak-L1 technique, which was developed by K. M. Rao. It is shown that any decomposition obtained by Rao’s method gives predictability of compensators without additional assumptions (like submartingality in the original Doob-Meyer theorem or finite energy in the Graversen-Rao theorem).