Abstract:
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.
Citation:
A. A. Gushchin, “The joint law of terminal values of a nonnegative submartingale and its compensator”, Teor. Veroyatnost. i Primenen., 62:2 (2017), 267–291; Theory Probab. Appl., 62:2 (2018), 216–235
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\by A.~A.~Gushchin
\paper The joint law of terminal values of a nonnegative submartingale and its compensator
\jour Teor. Veroyatnost. i Primenen.
\yr 2017
\vol 62
\issue 2
\pages 267--291
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\jour Theory Probab. Appl.
\yr 2018
\vol 62
\issue 2
\pages 216--235
\crossref{https://doi.org/10.1137/S0040585X97T988575}
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Linking options:
https://www.mathnet.ru/eng/tvp5108
https://doi.org/10.4213/tvp5108
https://www.mathnet.ru/eng/tvp/v62/i2/p267
This publication is cited in the following 7 articles:
D. A. Borzykh, “Joint distributions of generalized integrable increasing processes and their generalized compensators”, Theory Probab. Appl., 69:1 (2024), 1–24
A. A. Gushchin, D. A. Borzykh, “On the denseness of the subset of discrete distributions in a certain set of two-dimensional distributions”, Mod. Stoch., Theory Appl., 9:3 (2022), 265–277
A. A. Gushchin, “The joint law of a max-continuous local submartingale and its maximum”, Theory Probab. Appl., 65:4 (2021), 545–557
A. A. Gushchin, “Single jump filtrations and local martingales”, Mod. Stoch.-THeory Appl., 7:2 (2020), 135–156
“Abstracts of talks given at the 3rd International Conference on Stochastic Methods”, Theory Probab. Appl., 64:1 (2019), 124–169
A. A. Gushchin, “On possible relations between an increasing process and its compensator in the non-integrable case”, Russian Math. Surveys, 73:5 (2018), 928–930
“International conference on stochastic methods (Abstracts)”, Theory Probab. Appl., 62:4 (2018), 640–674
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