Work

Higher order approximation of nonlinear SPDEs with additive space-time white noise

Year: 2026

Type: article

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.

Source: The Annals of Probability

DOI: 10.1214/25-aop1818

Authors: Ana Djurdjevac, Máté Gerencsér, Helena Kremp

Institutions: Freie Universität Berlin, Weierstrass Institute for Applied Analysis and Stochastics

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: European Commission, Austrian Science Fund, Daimler und Benz Stiftung, HORIZON EUROPE European Research Council

Awards: Stochastic PDEs and Renormalisation, Regularisation by noise in discrete and continuous systems