Comments (1)
This is general
noise, as any component of X
can affect any component of dX
.
FWIW If you divide your equation by X(t)
, so as to obtain d log(X(t)) = A(t) d(t) + sum_j B_j(t) dW_j(t)
then this would become additive noise, which then admits higher-order solvers. (And in fact in this case, the right hand side becomes independent of X
, so I think you could even write down an analytical solution.)
Side note, torchsde requires that you bundle all diffusion terms together into the g
method. If you find yourself wanting to use solvers that make explicit use of decomposing the noise into multiple terms -- e.g. Ninomiya-Victoir -- then consider Diffrax. At least in principle this supports using multiple independent noise terms. (Although in practice none of the built-in solvers take advantage of this, but it'd be easy enough to write a solver that does if that is important to you.)
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