The Galerkin Approximation to Forward-Backward Stochastic Partial Differential Equations
Keywords:
forward-backward equations, partial differential equations, Galerkin approximation, forward-backward stochastic partial differential equations, stochastic differential equations
Abstract
In this paper, the authors utilized the Galerkin approximation scheme approach to solve a class of fully coupled forward-backward stochastic partial differential equations in an infinite dimensional functional setup.
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References
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Springer-Verlag, Berlin, 2007.
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Coefficients, Journal of Progressive Research in Mathematics, Vol 18, No. 1, April 2021.
Elliptic Partial Differential Equations, SIAM Journal on Numerical Analysis, Vol. 42, Iss. 2 (2004).
[2] Bl¨omker, D. and Jentzen, A. Galerkin Approximations for the Stochastic Burgers Equation, SIAM
Journal on Numerical Analysis, Vol. 51, No.1 (2013), 694-715.
[3] Breckner, H. Galerkin Approximation and the Strong Solution of the Navier-Stokes Equation, Journal
of Applied Mathematics and Stochastic Analysis, 13:3 (2000), 239–259.
[4] Chow, P. L. Stochastic Partial Differential Equations, Taylor & Francis Group, Boca Raton, 2007.
[5] Douglas, J., Ma, J. and Protter, P. Numerical methods for forward-backward stochastic differential
equations, The Annals of Applied Probability, Vol. 6, No. 3, 940-968, 1996.
[6] Grecksch, W. and Kloeden, P. E. Time-Discretised Galerkin Approximations of Parabolic Stochastic
PDEs, Bull. Austral. Math. Soc., Vol. 54, 79-85, 1996.
[7] Hu, Y. On the solution of forward-backward SDEs with monotone and continuous coefficients, Nonlinear
Anal., 42 (2000) 1–12.
[8] Hu, M. and Jiang, L. An efficient numerical method for forward-backward stochastic differential equations
driven by G-Brownian motion, Applied Numerical Mathematics, Vol. 164, 578-597, 2021.
[9] Lin, X., Chen, Y. and Huang, Y. Galerkin Spectral Approximation of Optimal Control Problems with
L2-norm Control Constraint, Applied Numerical Mathematics, Vol. 150, 418-432, 2020.
[10] Ma, J., Protter, P. and Yong, J. Solving Forward-Backward Stochastic Differential Equations Explicitly–
A Four Step Scheme, Prob. Th. & Rel. Fields, 98 (1994), 339–359.
[11] Ma, J., Yin, H., and Zhang, J. On non-Markovian forward-backward SDEs and Backward SPDEs,
Stochastic Processes and their Applications, 122 (2012) 3980-4004.
[12] Ma, J. and Yong, J. Adapted solution of a degenerate backward spde, with applications, Stochastic
Processes and their Applications, 70 (1997), 59–84.
[13] Ma, J. and Yong, J. On linear, degenerate backward stochastic partial differential equations, Probab.
Theory Related Fields 113 (1999), no. 2, 135–170.
[14] Ma, J. and Yong, J. Forward-Backward Stochastic Differential Equations and their Applications,
Springer-Verlag, Berlin, 2007.
[15] Yin, H. Solvability of Forward-Backward Stochastic Partial Differential Equations with Non-Lipschitz
Coefficients, Journal of Progressive Research in Mathematics, Vol 18, No. 1, April 2021.
Published
2023-04-23
How to Cite
Li, S., & Yin, H. (2023). The Galerkin Approximation to Forward-Backward Stochastic Partial Differential Equations. Journal of Progressive Research in Mathematics, 20(1), 49-62. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/2200
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