Open jakeyeung opened 9 months ago
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?
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