# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1703.06789