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Chen X, Ye W. A probabilistic representation for heat flow of harmonic map on manifolds with time-dependent Riemannian metric. Stat Probab Lett 2021. [DOI: 10.1016/j.spl.2021.109165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Yang X, Zhang Q, Zhang T. Reflected backward stochastic partial differential equations in a convex domain. Stoch Process Their Appl 2020. [DOI: 10.1016/j.spa.2020.05.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Ankirchner S, Engelhardt S, Fromm A, dos Reis G. The Skorokhod embedding problem for inhomogeneous diffusions. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2020. [DOI: 10.1214/19-aihp1012] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Ankirchner S, Fromm A, Kruse T, Popier A. Optimal position targeting via decoupling fields. ANN APPL PROBAB 2020. [DOI: 10.1214/19-aap1511] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Bayraktar E, Qiu J. Controlled reflected SDEs and Neumann problem for backward SPDEs. ANN APPL PROBAB 2019. [DOI: 10.1214/19-aap1465] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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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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Ekren I, Touzi N, Zhang J. Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part I. ANN PROBAB 2016. [DOI: 10.1214/14-aop999] [Citation(s) in RCA: 64] [Impact Index Per Article: 8.0] [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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