Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator
In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show that the solution to such infinite-dimensional BSDEs exists and is unique. The existence and uniqueness of the s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Online Access: | https://www.mdpi.com/2075-1680/11/10/536 |
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| author | Pei Zhang Adriana Irawati Nur Ibrahim Nur Anisah Mohamed |
| author_facet | Pei Zhang Adriana Irawati Nur Ibrahim Nur Anisah Mohamed |
| author_sort | Pei Zhang |
| collection | DOAJ |
| description | In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show that the solution to such infinite-dimensional BSDEs exists and is unique. The existence and uniqueness of the solution are established using Yosida approximations. Furthermore, as an application of the main result, we shall show that the backward stochastic partial differential equation driven by infinite-dimensional martingales with a continuous linear operator has a unique solution under the special condition that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">F</mi><mi>t</mi></msub></semantics></math></inline-formula>-progressively measurable generator <i>F</i> of the model we proposed in this paper equals zero. |
| first_indexed | 2024-03-09T20:42:45Z |
| format | Article |
| id | doaj.art-676180dfdcdd47d39ed6c09f406f49de |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T20:42:45Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj.art-676180dfdcdd47d39ed6c09f406f49de2023-11-23T22:53:58ZengMDPI AGAxioms2075-16802022-10-01111053610.3390/axioms11100536Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential OperatorPei Zhang0Adriana Irawati Nur Ibrahim1Nur Anisah Mohamed2Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, MalaysiaInstitute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, MalaysiaInstitute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, MalaysiaIn this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show that the solution to such infinite-dimensional BSDEs exists and is unique. The existence and uniqueness of the solution are established using Yosida approximations. Furthermore, as an application of the main result, we shall show that the backward stochastic partial differential equation driven by infinite-dimensional martingales with a continuous linear operator has a unique solution under the special condition that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">F</mi><mi>t</mi></msub></semantics></math></inline-formula>-progressively measurable generator <i>F</i> of the model we proposed in this paper equals zero.https://www.mdpi.com/2075-1680/11/10/536backward stochastic differential equations (BSDEs)variational inequalitiesmartingalessubdifferential operators |
| spellingShingle | Pei Zhang Adriana Irawati Nur Ibrahim Nur Anisah Mohamed Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator Axioms backward stochastic differential equations (BSDEs) variational inequalities martingales subdifferential operators |
| title | Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator |
| title_full | Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator |
| title_fullStr | Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator |
| title_full_unstemmed | Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator |
| title_short | Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator |
| title_sort | backward stochastic differential equations bsdes using infinite dimensional martingales with subdifferential operator |
| topic | backward stochastic differential equations (BSDEs) variational inequalities martingales subdifferential operators |
| url | https://www.mdpi.com/2075-1680/11/10/536 |
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