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All issues Volume 58 / No 1 (January-February 2024) ESAIM: M2AN, 58 1 (2024) 23-46 References
Open Access
Issue
ESAIM: M2AN
Volume 58, Number 1, January-February 2024
Page(s) 23 - 46
DOI https://doi.org/10.1051/m2an/2023100
Published online 16 January 2024
  1. P.R. Amestoy, A. Buttari, J.-Y. L’Excellent and T. Mary, Performance and scalability of the block low-rank multifrontal factorization on multicore architectures. ACM Trans. Math. Software 45 (2019) 26. [CrossRef] [Google Scholar]
  2. A. Bensoussan, Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions. Stochastics 9 (1983) 169–222. [CrossRef] [MathSciNet] [Google Scholar]
  3. C.-E. Bréhier, M. Hairer and A.M. Stuart, Weak error estimates for trajectories of SPDEs under spectral Galerkin discretization. J. Comput. Math. 36 (2018) 159–182. [Google Scholar]
  4. Y. Cao, Y. Jiang and Y. Xu, A fast discrete spectral method for stochastic partial differential equations. Adv. Comput. Math. 43 (2017) 973–998. [CrossRef] [MathSciNet] [Google Scholar]
  5. P.-L. Chow, Stochastic Partial Differential Equations. Advances in Applied Mathematics, 2nd edition. CRC Press, Boca Raton, FL (2015). [Google Scholar]
  6. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. Vol. 40 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2002). Reprint of the 1978 original [North-Holland, Amsterdam; MR0520174 (58 #25001)]. [Google Scholar]
  7. J. Cui and J. Hong, Strong and weak convergence rates of a spatial approximation for stochastic partial differential equation with one-sided Lipschitz coefficient. SIAM J. Numer. Anal. 57 (2019) 1815–1841. [CrossRef] [MathSciNet] [Google Scholar]
  8. J. Cui, J. Hong and Z. Liu, Strong convergence rate of finite difference approximations for stochastic cubic Schrödinger equations. J. Differ. Equ. 263 (2017) 3687–3713. [CrossRef] [Google Scholar]
  9. N. Dokuchaev, Backward parabolic Ito equations and the second fundamental inequality. Random Oper. Stoch. Equ. 20 (2012) 69–102. [CrossRef] [MathSciNet] [Google Scholar]
  10. K. Du and S. Tang, Strong solution of backward stochastic partial differential equations in C2 domains. Probab. Theory Related Fields 154 (2012) 255–285. [Google Scholar]
  11. T. Dunst and A. Prohl, The forward-backward stochastic heat equation: numerical analysis and simulation. SIAM J. Sci. Comput. 38 (2016) A2725–A2755. [CrossRef] [Google Scholar]
  12. N. El Karoui, S. Peng and M.C. Quenez, Backward stochastic differential equations in finance. Math. Finance 7 (1997) 1–71. [Google Scholar]
  13. M. Fuhrman and Y. Hu, Infinite horizon BSDEs in infinite dimensions with continuous driver and applications. J. Evol. Equ. 6 (2006) 459–484. [CrossRef] [MathSciNet] [Google Scholar]
  14. E. Gobet, J.-P. Lemor and X. Warin, A regression-based Monte Carlo method to solve backward stochastic differential equations. Ann. Appl. Probab. 15 (2005) 2172–2202. [CrossRef] [MathSciNet] [Google Scholar]
  15. M.D. Gunzburger and W. Zhao, Descriptions, discretizations, and comparisons of time/space colored and white noise forcings of the Navier-Stokes equations. SIAM J. Sci. Comput. 41 (2019) A2579–A2602. [CrossRef] [Google Scholar]
  16. Y. Hu, J. Ma and J. Yong, On semi-linear degenerate backward stochastic partial differential equations. Probab. Theory Related Fields 123 (2002) 381–411. [CrossRef] [MathSciNet] [Google Scholar]
  17. Y. Li, A high-order numerical method for BSPDEs with applications to mathematical finance. SIAM J. Financial Math. 13 (2022) 147–178. [CrossRef] [MathSciNet] [Google Scholar]
  18. Y. Li and S. Tang, Approximation of backward stochastic partial differential equations by a splitting-up method. J. Math. Anal. Appl. 493 (2021) 124518. [CrossRef] [Google Scholar]
  19. J. Ma and J. Yong, Adapted solution of a degenerate backward SPDE, with applications. Stochastic Process. Appl. 70 (1997) 59–84. [CrossRef] [MathSciNet] [Google Scholar]
  20. J. Ma and J. Yong, Forward-Backward Stochastic Differential Equations and Their Applications. Vol. 1702 of Lecture Notes in Mathematics, Springer-Verlag, Berlin (1999). [Google Scholar]
  21. E. Pardoux, Stochastic partial differential equations and filtering of diffusion processes. Stochastics 3 (1979) 127–167. [Google Scholar]
  22. É. Pardoux and S.G. Peng, Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14 (1990) 55–61. [CrossRef] [Google Scholar]
  23. E. Pardoux and S. Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equations, in Stochastic Partial Differential Equations and Their Applications, edited by B.L. Rozovskii and R.B. Sowers. Springer, Berlin Heidelberg, Berlin, Heidelberg (1992) 200–217. [CrossRef] [Google Scholar]
  24. S.G. Peng, A general stochastic maximum principle for optimal control problems. SIAM J. Control Optim. 28 (1990) 966–979. [CrossRef] [MathSciNet] [Google Scholar]
  25. S.G. Peng, Probabilistic interpretation for systems of quasilinear parabolic partial difierential equations. Stochastics Stochastics Rep. 37 (1991) 61–74. [CrossRef] [MathSciNet] [Google Scholar]
  26. C. Prévôt and M. Röckner, A Concise Course on Stochastic Partial Differential Equations. Vol. 1905 of Lecture Notes in Mathematics. Springer, Berlin (2007). [Google Scholar]
  27. T. Tang, W. Zhao and T. Zhou, Deferred correction methods for forward backward stochastic differential equations. Numer. Math. Theory Methods Appl. 10 (2017) 222–242. [CrossRef] [MathSciNet] [Google Scholar]
  28. X. Wang, W. Zhao and T. Zhou, Sinc-θ schemes for backward stochastic differential equations. SIAM J. Numer. Anal. 60 (2022) 1799–1823. [CrossRef] [MathSciNet] [Google Scholar]
  29. X. Yang and W. Zhao, Finite element methods for nonlinear backward stochastic partial differential equations and their error estimates. Adv. Appl. Math. Mech. 12 (2020) 1457–1480. [CrossRef] [MathSciNet] [Google Scholar]
  30. J. Yang, G. Zhang and W. Zhao, A first-order numerical scheme for forward-backward stochastic differential equations in bounded domains. J. Comput. Math. 36 (2018) 237–258. [CrossRef] [MathSciNet] [Google Scholar]
  31. W. Zhao, J. Wang and S. Peng, Error estimates of the θ-scheme for backward stochastic differential equations. Discrete Contin. Dyn. Syst. Ser. B 12 (2009) 905–924. [MathSciNet] [Google Scholar]
  32. W. Zhao, Y. Li and G. Zhang, A generalized θ-scheme for solving backward stochastic differential equations. Discrete Contin. Dyn. Syst. Ser. B 17 (2012) 1585–1603. [CrossRef] [MathSciNet] [Google Scholar]
  33. X.Y. Zhou, On the necessary conditions of optimal controls for stochastic partial differential equations. SIAM J. Control Optim. 31 (1993) 1462–1478. [CrossRef] [MathSciNet] [Google Scholar]

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