A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)
This implements the Ornstein Uhlenbeck Bridge as in https://arxiv.org/pdf/1011.0067.pdf%20page%2018.pdf
Furthermore there was some issues in the interpolate! function;
Wh was calculated as W[i] and W[i-1] respectively (forward, backward) meaning it is the value of W at the end of a step. This is inconsistent with the way solve calls the bridges. (Where Wh corresponds to Wend-W0)
the update of W conditioned on continous(W) was leading to wrong and inconsistent results compared to solve. The way the bridges are implemented are as a forward step, right?
interpolate! calls the bridge at t=t_end. While I think no bridge uses t, for consistency with solve I changed it to t0
-- none of these changes broke any tests
If these changes are sense full, they should also be applied to Z I guess.
This implements the Ornstein Uhlenbeck Bridge as in
https://arxiv.org/pdf/1011.0067.pdf%20page%2018.pdf
Furthermore there was some issues in the
interpolate!
function;Wh
was calculated asW[i]
andW[i-1]
respectively (forward, backward) meaning it is the value of W at the end of a step. This is inconsistent with the waysolve
calls the bridges. (Where Wh corresponds to Wend-W0)W
conditioned oncontinous(W)
was leading to wrong and inconsistent results compared tosolve
. The way the bridges are implemented are as a forward step, right?interpolate!
calls the bridge att=t_end
. While I think no bridge usest
, for consistency with solve I changed it tot0
-- none of these changes broke any tests
If these changes are sense full, they should also be applied to
Z
I guess.