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Luo P, Menoukeu-Pamen O, Tangpi L. Strong solutions of forward–backward stochastic differential equations with measurable coefficients. Stoch Process Their Appl 2022. [DOI: 10.1016/j.spa.2021.10.012] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Denis L, Matoussi A, Zhang J. Quasilinear Stochastic PDEs with two obstacles: Probabilistic approach. Stoch Process Their Appl 2021; 133:1-40. [DOI: 10.1016/j.spa.2020.11.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Wong CH, Yang X, Zhang J. Stochastic partial integral-differential equations with divergence terms. ELECTRON J PROBAB 2020. [DOI: 10.1214/20-ejp448] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Yang X, Zhang J. The obstacle problem for quasilinear stochastic PDEs with degenerate operator. Stoch Process Their Appl 2019. [DOI: 10.1016/j.spa.2018.08.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Dong Y, Yang X, Zhang J. The obstacle problem for quasilinear stochastic PDEs with Neumann boundary condition. STOCH DYNAM 2019. [DOI: 10.1142/s0219493719500394] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We prove the existence and uniqueness of solution to obstacle problem for quasilinear stochastic partial differential equations with Neumann boundary condition. Our method is based on the analytical techniques coming from parabolic potential theory. The solution is expressed as a pair [Formula: see text] where [Formula: see text] is a predictable continuous process which takes values in a proper Sobolev space and [Formula: see text] is a random regular measure satisfying minimal Skohorod condition.
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Affiliation(s)
- Yuchao Dong
- School of Mathematical Sciences, Fudan University, 220 Handan Rd., Yangpu District, Shanghai 200433, P. R. China
| | - Xue Yang
- School of Mathematics, Tianjin University, 135 Yaguan Road, Haihe Education Park, Tianjin 300350, P. R. China
| | - Jing Zhang
- School of Mathematical Sciences, Fudan University, 220 Handan Rd., Yangpu District, Shanghai 200433, P. R. China
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Denis L, Matoussi A, Zhang J. The existence and uniqueness result for quasilinear stochastic PDEs with obstacle under weaker integrability conditions. STOCH DYNAM 2015. [DOI: 10.1142/s0219493715500239] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We prove an existence and uniqueness result for quasilinear Stochastic PDEs with obstacle (in short OSPDE) under a weaker integrability condition on the coefficient and the barrier.
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Affiliation(s)
- Laurent Denis
- Fédération de Recherche 2962 du CNRS, Mathématiques des Pays de Loire, Laboratoire Manceau de Mathématiques, University of Maine, Avenue Olivier Messiaen, F-72085 Le Mans Cedex 9, France
| | - Anis Matoussi
- Fédération de Recherche 2962 du CNRS, Mathématiques des Pays de Loire, Laboratoire Manceau de Mathématiques, University of Maine, Avenue Olivier Messiaen, F-72085 Le Mans Cedex 9, France
- CMAP, Ecole Polytechnique, Palaiseau, France
| | - Jing Zhang
- School of Mathematical Science, Fudan University, Shanghai, P. R. China
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Affiliation(s)
- Denis Laurent
- Département de Mathématiques, Laboratoire de Statistiques et Processus E.A. 3263
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