The Annals of Probability· 2026Q1
Higher order approximation of nonlinear SPDEs with additive space-time white noise
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- Q1SCImago
- 2026year
Short summary
A new approximation scheme for nonlinear stochastic PDEs driven by additive space-time white noise achieves a temporal convergence rate of (almost) 1, a significant improvement over the previously optimal rate of 1/4.
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Key points
- A novel approximation scheme for nonlinear SPDEs with additive space-time white noise is introduced.
- The new scheme achieves a temporal convergence rate of (almost) 1 for a wide range of nonlinearities.
- This rate is a substantial improvement over the optimal rate of 1/4 achieved by schemes based on Wiener increments.
- The spatial convergence rate remains (almost) 1/2, consistent with existing literature.
AI-generated from the title and abstract; the full text is not read.
Abstract
We consider strong approximations of 1+1-dimensional stochastic PDEs driven by additive space-time white noise. It has long been proposed (Math. Comp. 70 (2001) 121–134; Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649–667), as well as observed in simulations, that approximation schemes based on samples from the stochastic convolution, rather than from increments of the underlying Wiener processes, should achieve significantly higher convergence rates with respect to the temporal timestep. The present paper proves this. For a large class of nonlinearities, with possibly superlinear growth, a temporal rate of (almost) 1 is proven, a major improvement on the rate 1/4 that is known to be optimal for schemes based on Wiener increments. The spatial rate remains (almost) 1/2, as it is standard in the literature.
The authors' abstract, as published at the source. The Annals of Probability, 2026 · DOI ↗
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Field: Finance
FinanceEconomics, Econometrics and Finance