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

Voir la notice de l'article provenant de la source Cambridge University Press

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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Bass, R. F., Probabilistic Techniques in Analysis, New York, Springer, 1995. Google Scholar

Dellacherie, C. and Meyer, R-A., Probabilités et Potentiel, Vol. 7, Paris, Hermann, 1975. Google Scholar

Dellacherie, C. and Meyer, R-A., Probabilités et Potentiel: Théorie des Martingales, Vol. 2, Paris, Hermann, 1980. Google Scholar

Doob, J .L., Stochastic Processes, New York, Wiley, 1953. Google Scholar

Doléans-Dade, C., Existence du processus croissant naturel associé à un potentiel de la classe (D), Zeit. Wahrschein. 9(1968), 309–314. Google Scholar

Ikeda, N. and Watanabe, S., Stochastic Differential Equations and Diffusion Processes, North Holland Kodansha, Amsterdam, 1981. Google Scholar

Meyer, P.-A., A decomposition theorem for supermartingales, Illinois J. Math. 6(1962), 193–205. Google Scholar

Meyer, P.-A., Decomposition of supermartingales: the uniqueness theorem, Illinois J. Math. 7(1963), 1—17. Google Scholar

[P] Protter, P., Stochastic Integration and Differential Equations, New York, Springer, 1990. Google Scholar

[R] Rao, K. M., On decomposition theorems of Meyer, Math. Scand. 24(1969), 66–78. Google Scholar

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