A new approximation method for solving stochastic differential equations

TL;DR

This paper introduces a new numerical approximation technique for solving Itô stochastic differential equations by subdividing time intervals and using quadratic polynomial approximations, with analysis of its key properties and promising test results.

Contribution

The paper proposes a novel quadratic polynomial-based method for SDEs, offering an alternative to existing techniques with analyzed convergence, consistency, and stability.

Findings

Method demonstrates promising accuracy in tests

Analyzed properties ensure reliability of the approach

Applicable to various SDE problems

Abstract

We present a novel solution method for It\^o stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main properties of the stochastic numerical methods, e.g. convergence, consistency, and stability are analyzed. We test the proposed method in SDE problem, demonstrating promising results.