Question about the "increment of Brownian motion" about torchsde HOT 4 CLOSED

Yep, that sounds correct to me.

from torchsde.

The parameter W is equal to B_{t_1} - B_{t_0}. For example it can be set to zero, so that BrownianInterval samples from a Brownian bridge.

In particular that should mean that it is unrelated to your use case. I believe sampling uncorrelated Brownian motion (via BrownianInterval) and then multiplying by sqrt(Q) should give you the distribution you're after.

from torchsde.

Thanks a lot for the clarification, @patrick-kidger.

A small follow-up:

Setting the diffusion function (g) equal to cholesky(Q)/sqrt(Q) in the SDE should produce the same effect, right? Assume that my state_dim and brownian_dim are equal and the SDE that I am interested in looks something like this:

dy(t) = f(t, y(t)) dt + dW(t)  with       y(t0) = y0    and    E[dW(t)dW(t)^T] = Qdt

from torchsde.

Awesome, thanks! Closing this.

from torchsde.