AN EXPONENTIAL WAGNER-PLATEN TYPE SCHEME FOR SPDES

作者：Becker, Sebastian^*; Jentzen, Arnulf; Kloeden, Peter E.

来源：SIAM Journal on Numerical Analysis, 2016, 54(4): 2389-2426.

DOI：10.1137/15M1008762

• exponential Wagner-Platen scheme
• stochastic partial differential equation
• SPDE
• strong convergence

The strong numerical approximation of semilinear stochastic partial differential equations (SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a number of results in the literature that show that Euler-type approximation methods converge, under suitable assumptions, to the exact solutions of such SPDEs with strong order 1/2 or at least with strong order 1/2 - epsilon, where epsilon > 0 is arbitrarily small. Recent results extend these results and show that Milstein-type approximation methods converge, under suitable assumptions, to the exact solutions of such SPDEs with strong order 1 - epsilon. It has also been shown that splitting up approximation methods converge, under suitable assumptions, with strong order 1 to the exact solutions of such SPDEs. In this article an exponential Wagner-Platen type numerical approximation method for such SPDEs is proposed and shown to converge, under suitable assumptions, with strong order 3/2 - epsilon to the exact solutions of such SPDEs.

• 出版日期2016
• 单位华中科技大学