A Combination of Finite Difference and Wong-Zakai Methods for Hyperbolic Stochastic Partial Differential Equations

Abstract

The present article focuses on the use of difference methods together with Wong-Zakai methods in order to approximate the solutions of stochastic hyperbolic differential equations of Itô type. We prove convergence, consistency, and stability for the schemes we use. Whereby the consistency and stability imply convergence.

Keywords:

• Consistency and stability
• Convergence in probability
• Stochastic partial differential equations of Itô type
• Wong-Zakai approximation

Mathematics Subject Classification:

• 60H15