<i>g</i>-Expectation for Conformable Backward Stochastic Differential Equations
In this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of <i>g</i>-expectation and give related properties...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/2/75 |
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| author | Mei Luo Michal Fečkan Jin-Rong Wang Donal O’Regan |
| author_facet | Mei Luo Michal Fečkan Jin-Rong Wang Donal O’Regan |
| author_sort | Mei Luo |
| collection | DOAJ |
| description | In this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of <i>g</i>-expectation and give related properties of <i>g</i>-expectation. In addition, we find that the properties of conformable backward stochastic differential equations can be deduced from the properties of the generator <i>g</i>. Finally, we extend the nonlinear Doob–Meyer decomposition theorem to more general cases. |
| first_indexed | 2024-03-09T22:36:58Z |
| format | Article |
| id | doaj.art-b9cc14fef64a487f80c46fd575361ebb |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T22:36:58Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-b9cc14fef64a487f80c46fd575361ebb2023-11-23T18:47:17ZengMDPI AGAxioms2075-16802022-02-011127510.3390/axioms11020075<i>g</i>-Expectation for Conformable Backward Stochastic Differential EquationsMei Luo0Michal Fečkan1Jin-Rong Wang2Donal O’Regan3Department of Mathematics, Guizhou University, Guiyang 550025, ChinaDepartment of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, SlovakiaDepartment of Mathematics, Guizhou University, Guiyang 550025, ChinaSchool of Mathematical and Statistical Sciences, National University of Ireland, 999014 Galway, IrelandIn this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of <i>g</i>-expectation and give related properties of <i>g</i>-expectation. In addition, we find that the properties of conformable backward stochastic differential equations can be deduced from the properties of the generator <i>g</i>. Finally, we extend the nonlinear Doob–Meyer decomposition theorem to more general cases.https://www.mdpi.com/2075-1680/11/2/75nonlinear expectation<i>g</i>-expectationDoob–Meyer decomposition theorem |
| spellingShingle | Mei Luo Michal Fečkan Jin-Rong Wang Donal O’Regan <i>g</i>-Expectation for Conformable Backward Stochastic Differential Equations Axioms nonlinear expectation <i>g</i>-expectation Doob–Meyer decomposition theorem |
| title | <i>g</i>-Expectation for Conformable Backward Stochastic Differential Equations |
| title_full | <i>g</i>-Expectation for Conformable Backward Stochastic Differential Equations |
| title_fullStr | <i>g</i>-Expectation for Conformable Backward Stochastic Differential Equations |
| title_full_unstemmed | <i>g</i>-Expectation for Conformable Backward Stochastic Differential Equations |
| title_short | <i>g</i>-Expectation for Conformable Backward Stochastic Differential Equations |
| title_sort | i g i expectation for conformable backward stochastic differential equations |
| topic | nonlinear expectation <i>g</i>-expectation Doob–Meyer decomposition theorem |
| url | https://www.mdpi.com/2075-1680/11/2/75 |
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