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Contents of PMS, Vol. 26, Fasc. 1,
pages 143 - 153
 

TOWARDS A GENERAL DOOB-MEYER DECOMPOSITION THEOREM

Adam Jakubowski

Abstract: Both the Doob-Meyer 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).

2000 AMS Mathematics Subject Classification: 60G07, 60G48, 60H05.

Key words and phrases: Doob-Meyer decomposition theorem, predictable compensator, processes with finite energy, martingales.

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