# The asymptotic error of chaos expansion approximations for stochastic differential equations

## TL;DR

This paper introduces a Wiener chaos expansion-based numerical scheme for stochastic differential equations, providing explicit error bounds and leveraging Malliavin calculus for analysis.

## Contribution

It presents a novel chaos expansion approximation method with explicit error bounds for SDEs, advancing numerical analysis in stochastic calculus.

## Key findings

- Derived explicit upper bounds for $L^2$ approximation error.
- Applied Malliavin calculus to analyze the chaos expansion approximation.
- Demonstrated the effectiveness of the method for square integrable SDEs.

## Abstract

In this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion in chaos order and in number of basis elements. We derive an explicit upper bound for the $L^2$ approximation error associated with our method. The proofs are based upon an application of Malliavin calculus.