Geodesic
The Doob-Meyer Decomposition Revisited
Canadian mathematical bulletin, Tome 39 (1996) no. 2, pp. 138-150

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DOI

A new proof is given of the Doob-Meyer decomposition of a supermartingale into martingale and decreasing parts. Although not the most concise proof, the proof is elementary in the sense that nothing more sophisticated than Doob's inequality is used. If the supermartingale is bounded and the jump times are totally inaccessible, then it is shown that discrete time approximations converge to the decreasing part in L2. The general case is handled by reduction to the above special case.
DOI : 10.4153/CMB-1996-018-8
Mots-clés : Primary: 60G07, secondary: 60G05, 60G44, supermartingales, Doob-Meyer decomposition, predictable, totally inaccessible, martingales 
Bass, Richard F. The Doob-Meyer Decomposition Revisited. Canadian mathematical bulletin, Tome 39 (1996) no. 2, pp. 138-150. doi: 10.4153/CMB-1996-018-8
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     title = {The {Doob-Meyer} {Decomposition} {Revisited}},
     journal = {Canadian mathematical bulletin},
     pages = {138--150},
     year = {1996},
     volume = {39},
     number = {2},
     doi = {10.4153/CMB-1996-018-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-018-8/}
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