Most Probable Phase Portraits of Stochastic Differential Equations and its Numerical Simulation

TL;DR

This paper introduces a practical method for obtaining and numerically simulating the most probable phase portraits of stochastic differential equations, using Euler-Maruyama, with accessible examples.

Contribution

It provides a straightforward approach and numerical implementation for visualizing the most probable phase portraits of SDEs, enhancing understanding and accessibility.

Findings

Method for obtaining most probable phase portraits

Numerical simulation using Euler-Maruyama method

Accessible examples demonstrating the approach

Abstract

A practical and accessible introduction to most probable phase portraits is given. The reader is assumed to be familiar with stochastic differential equations and Euler-Maruyama method in numerical simulation. The article first introduce the method to obtain most probable phase portraits and then give its numerical simulation which is based on Euler-Maruyama method. All of these are given by examples and easy to understand.