# RDE versus SDE

**URL:** <https://discourse.julialang.org/t/rde-versus-sde/40150>\
**Category:** New to Julia\
**Tags:** sde, rode\
**Created:** [May 25, 2020, 7:13pm UTC](https://discourse.julialang.org/t/rde-versus-sde/40150 "2020-05-25T19:13:24Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![erlebach](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/erlebach/32/12973_2.png) [@erlebach](https://discourse.julialang.org/u/erlebach)\
**Post date:** [May 25, 2020, 7:13pm UTC](https://discourse.julialang.org/t/rde-versus-sde/40150/1 "2020-05-25T19:13:24Z")

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What is the difference between a Random Differential Equation and a Stochastic Differential Equation?  
I read the documentation of DifferentialEquations.jl, but I cannot wrap my head around it. Thanks.

Gordon

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**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [May 25, 2020, 7:15pm UTC](https://discourse.julialang.org/t/rde-versus-sde/40150/2 "2020-05-25T19:15:21Z")

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This tutorial by Trefethen may be helpful: [From random functions to SDEs » Chebfun](https://www.chebfun.org/examples/ode-random/Random2SDE.html)

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**Author:** ![erlebach](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/erlebach/32/12973_2.png) [@erlebach](https://discourse.julialang.org/u/erlebach)\
**Post date:** [May 25, 2020, 7:23pm UTC](https://discourse.julialang.org/t/rde-versus-sde/40150/3 "2020-05-25T19:23:54Z")

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Thank you!

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 25, 2020, 7:47pm UTC](https://discourse.julialang.org/t/rde-versus-sde/40150/4 "2020-05-25T19:47:50Z")

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Random ordinary differential equations are a generalization of SDEs. SDEs require a linear relationship to the Brownian terms: it’s always g(X)\*dW, while RODEs do g(X,zeta) where zeta is some noise process. Any SDE can be written as an RODE where zeta is an Ornstein-Uhlenbeck process. This is a good quick intro:

> **[neckel\_GUtech\_2016.pdf](https://www5.in.tum.de/pub/neckel_GUtech_2016.pdf)**
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> 697.29 KB

RODEs then give a good way to analyze numerical methods which extend beyond Wiener processes as noise, i.e. Levy processes and stuff like, and can be a more natural way to write models with randomness on parameters in a way that gives a nonlinear relationship to the noise.

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**Author:** ![ericphanson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ericphanson/32/215186_2.png) [@ericphanson](https://discourse.julialang.org/u/ericphanson)\
**Post date:** [May 25, 2020, 7:59pm UTC](https://discourse.julialang.org/t/rde-versus-sde/40150/5 "2020-05-25T19:59:12Z")

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Wrong link, I think 🙂

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 25, 2020, 8:05pm UTC](https://discourse.julialang.org/t/rde-versus-sde/40150/6 "2020-05-25T20:05:36Z")

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Haha thanks.

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**Author:** ![erlebach](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/erlebach/32/12973_2.png) [@erlebach](https://discourse.julialang.org/u/erlebach)\
**Post date:** [May 25, 2020, 9:24pm UTC](https://discourse.julialang.org/t/rde-versus-sde/40150/7 "2020-05-25T21:24:00Z")

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What is the correct link? 🙂

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 25, 2020, 9:29pm UTC](https://discourse.julialang.org/t/rde-versus-sde/40150/8 "2020-05-25T21:29:57Z")

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I edited it. I accidentally linked to CompatHelper stuff 🙂