Geodesic
The joint law of terminal values of a nonnegative submartingale and its compensator
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 267-291

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We characterize the set $W$ of possible joint laws of terminal values of a nonnegative submartingale $X$ of class $(D)$, starting at 0, and the predictable increasing process (compensator) from its Doob–Meyer decomposition. The set of possible values remains the same under certain additional constraints on $X$, for example, under the condition that $X$ is an increasing process or a squared martingale. Special attention is paid to extremal (in a certain sense) elements of the set $W$ and to the corresponding processes. We relate also our results with Rogers's results on the characterization of possible joint values of a martingale and its maximum.
Keywords: increasing process, time-change, comonotonicity, compensator, nonnegative submartingale, Doob–Meyer decomposition. 
@article{TVP_2017_62_2_a2,
     author = {A. A. Gushchin},
     title = {The joint law of terminal values of a nonnegative submartingale and its compensator},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {267--291},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a2/}
}
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A. A. Gushchin. The joint law of terminal values of a nonnegative submartingale and its compensator. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 267-291. http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a2/