RDE versus SDE

New to Julia
,
1

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

2

This tutorial by Trefethen may be helpful: From random functions to SDEs » Chebfun

1 Like
3

Thank you!

4

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:

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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5

Wrong link, I think :slight_smile:

6

Haha thanks.

7

What is the correct link? :slight_smile:

8

I edited it. I accidentally linked to CompatHelper stuff :slight_smile: