patrick-kidger
Simulate SDE with white noise?
Hi,
I was wondering if it's possible to simulate SDEs using white noise, rather than the brownian motion (e.g. brownian_motion = VirtualBrownianTree(t0, t1, tol=1e-3, shape=(), key=jrandom.PRNGKey(0))) shown in the docs?
I searched around the github but did not see any functions related to white noise.
Kindest regards,
Jake
Hey there! What does "simulate an SDE using white noise" mean to you? What precise numerical opertion are you looking to describe?
(For context, I usually think of white noise as being "the derivative of Brownian motion". So formally, it is the X given by (X, φ) = - integral w(t) φ'(t) dt, using integration by parts to move the derivative on to the actually-differentiable test function.)
Hi,
Yes I am thinking of white noise as the derivative of Brownian motion.
Practically, I would like to compare SDEs simulated with Brownian motion (where 95% quantiles increase proportionally to square root of time) versus with white noise (95% quantiles are constant over time). I was wondering how to do that with diffrax.
Do you have a reference for the mathematical operation you're trying to perform?