A novel approach to construct numerical methods for stochastic differential equations

TL;DR

This paper introduces a new numerical method for solving stochastic differential equations, providing an explicit scheme that converges where traditional Euler methods fail, especially for super linear SDEs.

Contribution

The paper presents a novel numerical approach that improves convergence for super linear SDEs where existing methods diverge.

Findings

The new method successfully solves super linear SDEs where Euler diverges.

The explicit scheme demonstrates better stability and convergence properties.

The approach extends the applicability of numerical solutions for complex SDEs.

Abstract

In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.