Celebratio Mathematica — Yor — Complete Bibliography

Complete Bibliography

Works connected to Joseph L. Doob

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A. Nikeghbali and M. Yor: “Doob’s maximal identity, multiplicative decompositions and enlargements of filtrations,” pp. 791–814 in Joseph Doob: A collection of mathematical articles in his memory, published as Ill. J. Math. 50 : 1–4. Issue edited by J. Burkholder. University of Illinois at Urbana-Champaign, 2006. MR 2247846 Zbl 1101.60059 incollection

In the theory of progressive enlargements of filtrations, the supermartingale \[ Z_t = \mathbf{P}(g\gt t \mid \mathcal{F}_t) \] associated with an honest time \( g \), and its additive (Doob–Meyer) decomposition, play an essential role. In this paper, we propose an alternative approach, using a multiplicative representation for the supermartingale \( Z_t \), based on Doob’s maximal identity. We thus give new examples of progressive enlargements. Moreover, we give, in our setting, a proof of the decomposition formula for martingales, using initial enlargement techniques, and use it to obtain some path decompositions given the maximum or minimum of some processes.

Joseph L. Doob	Related	Volume
Ashkan Nikeghbali	Related

M. Yor: “Joseph Leo Doob (27 février 1910–7 juin 2004)” [Joseph Leo Doob (27 Feburary 1910–7 June 2004)], Gaz. Math. 114 (2007), pp. 33–39. MR 2361707 Zbl 1221.01089 article

M. Yor: “J. L. Doob (27 February 1910–7 June 2004),” Ann. Probab. 37 : 5 (2009), pp. 1664–1670. Translation of French original published in Gaz. Math. 114 (2007). MR 2561429 Zbl 1176.60004 article