Time discretization of FBSDE with polynomial growth drivers and reaction-diffusion PDEs. (English) Zbl 1342.65011
This is a nice paper with some deep mathematical time discretization analysis. The authors consider the error analysis of numerical methods for systems of forwards, backwards stochastic differential equations with polynomial growth drivers. They first extend the canonical Zhang path regularity theorem to the polynomial case. The authors then examine the stability of the class of \(\theta\) methods and show that \(\theta\geq 1/2\) is essential for stability in the polynomial case and also prove a higher convergence rate for the case \(\theta=1/2\).
Finally, a tamed version of the explicit Euler method is constructed under which it is stable and convergent. A general result for the global error in a non-Lipschitz framework is derived and some simple numerical tests conclude the paper.
Finally, a tamed version of the explicit Euler method is constructed under which it is stable and convergent. A general result for the global error in a non-Lipschitz framework is derived and some simple numerical tests conclude the paper.
Reviewer: Kevin Burrage (Brisbane)
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
Keywords:
FBSDE; monotone driver; polynomial growth; time discretization; path regularity; calculus of variations; numerical schemesReferences:
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