Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schrödinger and linearized stochastic Korteweg-de Vries equations
Provides sharp error bounds for numerical approximations of stochastic evolution equations, benefiting researchers in stochastic analysis and numerical methods for SPDEs.
The paper establishes essentially sharp weak convergence rates for noise discretizations of a wide class of stochastic evolution equations, including nonlinear stochastic wave, HJMM, stochastic Schrödinger, and linearized stochastic Korteweg-de Vries equations, improving upon previous suboptimal rates.
We establish weak convergence rates for noise discretizations of a wide class of stochastic evolution equations with non-regularizing semigroups and additive or multiplicative noise. This class covers the nonlinear stochastic wave, HJMM, stochastic Schrödinger and linearized stochastic Korteweg-de Vries equation. For several important equations, including the stochastic wave equation, previous methods give only suboptimal rates, whereas our rates are essentially sharp.