Approximation of backward stochastic partial differential equations by a splitting-up method

Li, Yunzhang; Tang, Shanjian

doi:10.1016/j.jmaa.2020.124518

Cited by 7 publications

(5 citation statements)

References 21 publications

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“…Combining (53) and the above estimates of η 1 , η 2 and η 3 yields (51). Finally, using ( 50) and ( 51) proves (33) and thus concludes the proof of Theorem 4.1.…”

Section: Proof Of Theorem 41supporting

confidence: 67%

“…Since this scheme uses the eigenvectors of the Laplace operator, its application appears to be limited. Li and Tang [33] developed a splitting-up method for solving backward stochastic partial differential equations. We refer to [15,31,32,45,44,55] for a few works containing the numerical analysis of some linear backward stochastic parabolic equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation

Li¹,

Xie²

2021

Preprint

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This paper studies the convergence of a spatial semidiscretization for a backward semilinear stochastic parabolic equation. The filtration is general, and the spatial semidiscretization uses the standard continuous piecewise linear finite element method. Firstly, higher regularity of the solution to the continuous equation is derived. Secondly, the first-order spatial accuracy is derived for the spatial semidiscretization. Thirdly, an application of the theoretical results to a stochastic linear quadratic control problem is presented.

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“…Combining (53) and the above estimates of η 1 , η 2 and η 3 yields (51). Finally, using ( 50) and ( 51) proves (33) and thus concludes the proof of Theorem 4.1.…”

Section: Proof Of Theorem 41supporting

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation

Li¹,

Xie²

2021

Preprint

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show abstract

“…In recent years, great efforts have been made for constructing and analyzing effective numerical schemes for BSDEs [14,27,28,32] and stochastic partial differential equations (SPDEs) [3,4,7,8,15], etc. As a counterpart, BSPDEs are few numerically studied, but there are still some literature, among which are Euler method [11,29], splitting-up method [18], and [17] for some recent developments.…”

Section: Introductionmentioning

confidence: 99%

A generalized finite element θ-scheme for backward stochastic partial differential equations and its error estimates

Sun,

Zhao,

Zhao

2024

ESAIM: M2AN

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In this paper, we study numerical methods for solving a class of nonlinear backward stochastic partial differential equations. By utilizing finite element methods in space and $\theta$-scheme in time, the proposed scheme forms a generalized spatio-temporal full discrete scheme, which can be solved in parallel. We rigorously prove the boundedness and error estimates, and obtain the optimal convergence rates in both time (first order/second order) and space ($k+1$, $k$ in $L^2$ and $H^1$, respectively). Numerical results are finally provided to demonstrate the effectiveness of the proposed scheme and validate the theoretical analyses.The analytical techniques we presented can be directly applied to other more complicated BSPDEs.

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“…Wang [27,28] analyzed a time-discretized Galerkin approximation of a semilinear backward stochastic parabolic equation and a timediscretization Galerkin approximation of a linear backward stochastic parabolic equation. Recently, Li and Tang [19] developed a splitting-up method for backward stochastic parabolic equations, where no convergence rate was derived for the general nonlinear case.…”

Section: Introductionmentioning

confidence: 99%

Discretization of a distributed optimal control problem with a stochastic parabolic equation driven by multiplicative noise

Li¹

2020

Preprint

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Approximation of backward stochastic partial differential equations by a splitting-up method

Cited by 7 publications

References 21 publications

Convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation

Convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation

A generalized finite element θ-scheme for backward stochastic partial differential equations and its error estimates

Discretization of a distributed optimal control problem with a stochastic parabolic equation driven by multiplicative noise

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