English

Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schr\"odinger and linearized stochastic Korteweg-de Vries equations

Probability 2019-04-10 v4 Numerical Analysis

Abstract

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 Schr\"odinger 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.

Keywords

Cite

@article{arxiv.1710.01273,
  title  = {Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schr\"odinger and linearized stochastic Korteweg-de Vries equations},
  author = {Philipp Harms and Marvin S. Müller},
  journal= {arXiv preprint arXiv:1710.01273},
  year   = {2019}
}

Comments

26 pages, minor revision