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Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 2, Pages 267–291 (Mi tvp5108)  

This article is cited in 4 scientific papers (total in 4 papers)

The joint law of terminal values of a nonnegative submartingale and its compensator

A. A. Gushchin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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.

Keywords: increasing process, time-change, comonotonicity, compensator, nonnegative submartingale, Doob–Meyer decomposition.

Funding Agency Grant Number
Russian Science Foundation 14-21-00162
This work was supported by the Russian Science Foundation under grant 14-21-00162.


DOI: https://doi.org/10.4213/tvp5108

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English version:
Theory of Probability and its Applications, 2018, 62:2, 216–235

Bibliographic databases:

Received: 16.01.2017
Accepted:16.02.2017

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. “International conference on stochastic methods (Abstracts)”, Theory Probab. Appl., 62:4 (2018), 640–674  mathnet  crossref  crossref  isi  elib
    2. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. “Abstracts of talks given at the 3rd International Conference on Stochastic Methods”, Theory Probab. Appl., 64:1 (2019), 124–169  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. A. Guschin, “Sovmestnoe raspredelenie maks-nepreryvnogo lokalnogo submartingala i ego maksimuma”, Teoriya veroyatn. i ee primen., 65:4 (2020), 693–709  mathnet  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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