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Relevant bibliographies by topics / Fully coupled forward-backward parabolic equations

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Academic literature on the topic 'Fully coupled forward-backward parabolic equations'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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Journal articles on the topic "Fully coupled forward-backward parabolic equations"

1

Ya., Belopolskaya. "Probabilistic Approaches to Nonlinear Parabolic Equations in Jet-Bundles." Global and Stochastic Analysis 1, no. 1 (2014): 1–40. https://doi.org/10.5281/zenodo.7673376.

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We develop two probabilistic approaches that allows to construct a solution of the Cauchy problem for a class of fully nonlinear second order PDEs. Within the first one we reduce an original PDE to a quasilinear PDE in the second order jet-bundle and construct a probabilistic counterpart in terms of forward stochastic equations for the resulting Cauchy problem. The second is based on a reduction to a semilinear  PDE that allows to reduce the original problem to a fully coupled forward-backward BSDE.

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2

Xiao, Lishun, Shengjun Fan, and Dejian Tian. "A probabilistic approach to quasilinear parabolic PDEs with obstacle and Neumann problems." ESAIM: Probability and Statistics 24 (2020): 207–26. http://dx.doi.org/10.1051/ps/2019023.

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In this paper, by a probabilistic approach we prove that there exists a unique viscosity solution to obstacle problems of quasilinear parabolic PDEs combined with Neumann boundary conditions and algebra equations. The existence and uniqueness for adapted solutions of fully coupled forward-backward stochastic differential equations with reflections play a crucial role. Compared with existing works, in our result the spatial variable of solutions of PDEs lives in a region without convexity constraints, the second order coefficient of PDEs depends on the gradient of the solution, and the required

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3

Casserini, Matteo, and Gechun Liang. "Fully coupled forward–backward stochastic dynamics and functional differential systems." Stochastics and Dynamics 15, no. 02 (2015): 1550006. http://dx.doi.org/10.1142/s0219493715500069.

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This paper introduces and solves a general class of fully coupled forward–backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different types of forward–backward stochastic differential equations (FBSDEs) that do not fit in the classical setting. In our approach, the equations are running in the same time direction rather than in a forward and backward way, and the conflicting nature of the structure of FBSDEs is therefore avoided.

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4

Wei, Qingmeng. "The Optimal Control Problem with State Constraints for Fully Coupled Forward-Backward Stochastic Systems with Jumps." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/216053.

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We focus on the fully coupled forward-backward stochastic differential equations with jumps and investigate the associated stochastic optimal control problem (with the nonconvex control and the convex state constraint) along with stochastic maximum principle. To derive the necessary condition (i.e., stochastic maximum principle) for the optimal control, first we transform the fully coupled forward-backward stochastic control system into a fully coupled backward one; then, by using the terminal perturbation method, we obtain the stochastic maximum principle. Finally, we study a linear quadratic

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5

Wang, Mingcan, and Xiangjun Wang. "Hybrid Neural Networks for Solving Fully Coupled, High-Dimensional Forward–Backward Stochastic Differential Equations." Mathematics 12, no. 7 (2024): 1081. http://dx.doi.org/10.3390/math12071081.

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The theory of forward–backward stochastic differential equations occupies an important position in stochastic analysis and practical applications. However, the numerical solution of forward–backward stochastic differential equations, especially for high-dimensional cases, has stagnated. The development of deep learning provides ideas for its high-dimensional solution. In this paper, our focus lies on the fully coupled forward–backward stochastic differential equation. We design a neural network structure tailored to the characteristics of the equation and develop a hybrid BiGRU model for solvi

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6

Min, Hui, Ying Peng, and Yongli Qin. "Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle." Abstract and Applied Analysis 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/839467.

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We discuss a new type of fully coupled forward-backward stochastic differential equations (FBSDEs) whose coefficients depend on the states of the solution processes as well as their expected values, and we call them fully coupled mean-field forward-backward stochastic differential equations (mean-field FBSDEs). We first prove the existence and the uniqueness theorem of such mean-field FBSDEs under some certain monotonicity conditions and show the continuity property of the solutions with respect to the parameters. Then we discuss the stochastic optimal control problems of mean-field FBSDEs. Th

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7

Ji, Shaolin, and Shuzhen Yang. "Solutions for functional fully coupled forward–backward stochastic differential equations." Statistics & Probability Letters 99 (April 2015): 70–76. http://dx.doi.org/10.1016/j.spl.2015.01.009.

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8

Lin, X.-Y., Q.-X. Sun, and X.-R. Wang. "The robustness of fully coupled forward-backward stochastic differential equations." Journal of Physics: Conference Series 96 (February 1, 2008): 012207. http://dx.doi.org/10.1088/1742-6596/96/1/012207.

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9

Li, Juan. "FULLY COUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH GENERAL MARTINGALE." Acta Mathematica Scientia 26, no. 3 (2006): 443–50. http://dx.doi.org/10.1016/s0252-9602(06)60068-4.

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10

Al-Hussein, AbdulRahman, and Boulakhras Gherbal. "Existence and uniqueness of the solutions of forward-backward doubly stochastic differential equations with Poisson jumps." Random Operators and Stochastic Equations 28, no. 4 (2020): 253–68. http://dx.doi.org/10.1515/rose-2020-2044.

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AbstractThe paper addresses a system of nonlinear fully coupled forward-backward doubly stochastic differential equations with Poisson jumps. These equations are allowed to live in Euclidean spaces of different dimensions, and the system is Markovian in the sense that the terminal value of the backward equation depends on the terminal value of the solution of the forward one. Under some monotonicity conditions we establish the existence and uniqueness of strong solutions of such equations by using a continuation method.

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