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math.NA2026
Analysis of an exponential integrator for stochastic PDEs driven by Riesz noise
Charles-Edouard Bréhier, David Cohen, Lluís Quer-Sardanyons +1
We present and study an explicit exponential integrator for parabolic SPDEs in any dimension driven by a Gaussian noise which is white in time and with spatial correlation given by…
math.NA2025
Preconditioning for the high-order sampling of the invariant distribution of parabolic semilinear SPDEs
Charles-Edouard Bréhier, Adrien Busnot Laurent, Arnaud Debussche +1
For a class of ergodic parabolic semilinear stochastic partial differential equations (SPDEs) with gradient structure, we introduce a preconditioning technique and design high-orde…
math.NA2025
Analysis of splitting schemes for stochastic evolution equations with non-Lipschitz nonlinearities driven by fractional noise
Xiao-Li Ding, Charles-Edouard Bréhier, Dehua Wang
We propose a novel time-splitting scheme for a class of semilinear stochastic evolution equations driven by cylindrical fractional noise. The nonlinearity is decomposed as the sum…