Consistency and Asymptotic Normality of Stochastic Euler Schemes for Ordinary Differential Equations

TL;DR

This paper investigates stochastic Euler schemes for ordinary differential equations, establishing their consistency, convergence rate, and asymptotic normality to ensure reliable numerical solutions.

Contribution

It provides rigorous proofs of consistency, convergence rate, and asymptotic normality for stochastic Euler schemes, advancing theoretical understanding.

Findings

Proves the schemes are consistent

Establishes the rate of convergence

Shows asymptotic normality of the schemes

Abstract

General stochastic Euler schemes for ordinary differential equations are studied. We give proofs on the consistency, the rate of convergence and the asymptotic normality of these procedures.