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[07x12] Intro to Stochastic Differential Equations in Julia using DifferentialEquations.jl and Pluto

Learn how to solve Stochastic Differential Equations (SDE) in Julia by using the DifferentialEquations.jl package and a Pluto notebook. Until now, every solution to a differential equation that we've seen has been deterministic, meaning that the solution was determined without any randomness. So, if you used the same initial settings that I used, then your results should've been the same as my results. But the real world is not that predictable. In order to model real world simulations, we need the ability to include some random noise in our solutions. One way to do that is to use SDEs, which is a Differential Equation plus some random noise. In this tutorial, you'll learn how to solve SDEs in Julia by using a modified version of the Continuous Compound Interest problem from Episode 704. You'll also build a model in a Pluto notebook that you can use to modify parameters to better understand how SDEs work. Prerequisites: Knowledge about Differential Equations is not required. Basic knowledge about Julia Programming Language and Pluto Notebooks is required. Basic knowledge about how to use the DifferentialEquations.jl package to solve both First Order, Second Order Ordinary Differential Equations and Systems of Differential Equations is required. 00:00 Intro 01:16 Prerequisites 01:47 Launch Pluto 03:28 Define Problems 08:17 Solve Problems 10:06 Plot Solutions 16:20 Recap 18:27 Outro ######################################## Links for this tutorial ######################################## Code for this tutorial https://github.com/julia4ta/tutorials... Wikipedia Article on Stochastic Differential Equation https://en.wikipedia.org/wiki/Stochas... DifferentialEquations.jl (docs) https://diffeq.sciml.ai/stable/ DifferentialEquations.jl (GitHub) https://github.com/SciML/Differential... ######################################## Links for this series ######################################## Link to Series 7 Playlist [Julia Differential Equations for Beginners]    • [07x01] How to Install Julia and Plut...   The Julia Programming Language https://julialang.org/ https://docs.julialang.org/en/v1/    / thejulialanguage   DifferentialEquations.jl https://diffeq.sciml.ai/stable/ https://github.com/SciML/Differential... Pluto.jl (GitHub) https://github.com/fonsp/Pluto.jl ######################################## Join Button (Channel Membership): If you like what I do, then please consider Joining and becoming a Channel Member.    / @doggodotjl   Thank you!