Optimal rate of convergence for stochastic Burgers-type equations

Abstract

Recently, a solution theory for one-dimensional stochastic PDEs of Burgers type driven by space-time white noise was developed. In particular, it was shown that natural numerical approximations of these equations converge and that their convergence rate in the uniform topology is arbitrarily close to $\frac{1}{6}$. In the present article we improve this result in the case of additive noise by proving that the optimal rate of convergence is arbitrarily close to $\frac{1}{2}$.

36 pages

Cited by in corpus (4)

• Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations
• Transient Growth in Stochastic Burgers Flows
• Strong convergence of parabolic rate $1$ of discretisations of stochastic Allen-Cahn-type equations
• Large time behavior of strong solutions for stochastic Burgers equation