From d2fc43f6d66d312b4b9732c1435c9baccf82ae45 Mon Sep 17 00:00:00 2001 From: Navdeep Rana Date: Thu, 14 Dec 2023 15:50:00 +0100 Subject: [PATCH] Update sde_example.md --- docs/src/tutorials/sde_example.md | 9 ++++----- 1 file changed, 4 insertions(+), 5 deletions(-) diff --git a/docs/src/tutorials/sde_example.md b/docs/src/tutorials/sde_example.md index adb3767d4..9e13cf607 100644 --- a/docs/src/tutorials/sde_example.md +++ b/docs/src/tutorials/sde_example.md @@ -145,15 +145,14 @@ du = f(u,p,t)dt + g(u,p,t)dW, where `g` is now a matrix of values, is numerically integrated in the same way as ODEs. A common scenario is when we have diagnol noise, which is the default for DifferentialEquations.jl. Physically this means that -every variable in the system gets a random kick. Consequently, `g` is a +every variable in the system gets a different random kick. Consequently, `g` is a diagonal matrix and we can handle this in a simple manner by defining the deterministic part `f(du,u,p,t)` and the stochastic part `g(du2,u,p,t)` as in-place functions. -For example, the Lorenz equation with additive noise has the same deterministic -portion as the Lorenz equations, but adds an additive noise, which is simply -`3*N(0,dt)` where `N` is the normal distribution `dt` is the time step, to each -step of the equation. This is done via: +Consider for example a stochastic variant of the Lorenz equations, where we introduce a +simple additive noise to each of `x,y,z`, which is simply `3*N(0,dt)`. Here `N` is the normal +distribution and `dt` is the time step. This is done as follows: ```@example sde2 using DifferentialEquations