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Qiu J. Weak solution for a class of fully nonlinear stochastic Hamilton–Jacobi–Bellman equations. Stoch Process Their Appl 2017. [DOI: 10.1016/j.spa.2016.09.010] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Yin H. Forward–backward stochastic partial differential equations with non-monotonic coefficients. STOCH DYNAM 2016. [DOI: 10.1142/s0219493716500258] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper we study the solvability of a class of fully-coupled forward–backward stochastic partial differential equations (FBSPDEs) with non-monotonic coefficients. These FBSPDEs cannot be put into the framework of stochastic evolution equations in general, and the usual decoupling methods for the Markovian forward–backward SDEs are difficult to apply. We prove the well-posedness of such FBSPDEs by using the method of continuation. Contrary to the common belief, we show that the usual monotonicity assumption can be removed by a change of the diffusion term.
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Affiliation(s)
- Hong Yin
- Department of Mathematics, State University of New York, Brockport, NY 14420, USA
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Tang S, Wei W. On the Cauchy problem for backward stochastic partial differential equations in Hölder spaces. ANN PROBAB 2016. [DOI: 10.1214/14-aop976] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Ma J, Wu Z, Zhang D, Zhang J. On well-posedness of forward–backward SDEs—A unified approach. ANN APPL PROBAB 2015. [DOI: 10.1214/14-aap1046] [Citation(s) in RCA: 67] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Englezos N, Frangos NE, Kartala XI, Yannacopoulos AN. Stochastic Burgers PDEs with random coefficients and a generalization of the Cole–Hopf transformation. Stoch Process Their Appl 2013. [DOI: 10.1016/j.spa.2013.03.001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Du K, Zhang Q. Semi-linear degenerate backward stochastic partial differential equations and associated forward–backward stochastic differential equations. Stoch Process Their Appl 2013. [DOI: 10.1016/j.spa.2013.01.005] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Du K, Tang S. Strong solution of backward stochastic partial differential equations in C 2 domains. Probab Theory Relat Fields 2011. [DOI: 10.1007/s00440-011-0369-0] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Du K, Meng Q. A revisit to W2n-theory of super-parabolic backward stochastic partial differential equations in Rd. Stoch Process Their Appl 2010. [DOI: 10.1016/j.spa.2010.06.001] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Sundar P, Yin H. Existence and uniqueness of solutions to the backward 2D stochastic Navier–Stokes equations. Stoch Process Their Appl 2009. [DOI: 10.1016/j.spa.2008.06.007] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Confortola F. Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity. Stoch Process Their Appl 2007. [DOI: 10.1016/j.spa.2006.09.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Fuhrman M. Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control. ANN PROBAB 2002. [DOI: 10.1214/aop/1029867132] [Citation(s) in RCA: 94] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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