4 papers
Strong and weak rates of convergence in the Smoluchowski--Kramers approximation for stochastic partial differential equations
Charles-Edouard Bréhier, Ziyi Lei
We consider a class of stochastic damped semilinear wave equations, in the small-mass limit. It has previously been established that the solution converges to the solution of a sto…
Analysis of an exponential integrator for stochastic PDEs driven by Riesz noise
Charles-Edouard Bréhier, David Cohen, LluÃs 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…
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…
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…