Mathematical Specification of a RODE Problem
To define a RODE Problem, you simply need to give the function $f$ and the initial condition $u₀$ which define an ODE:
W(t) is a random process.
f should be specified as
f(t,u,W) (or in-place as
u₀ should be an AbstractArray (or number) whose geometry matches the desired geometry of
u. Note that we are not limited to numbers or vectors for
u₀; one is allowed to provide
u₀ as arbitrary matrices / higher dimension tensors as well.
RODEProblem(f,u0,tspan,noise=WHITE_NOISE,noise_prototype=nothing,callback=nothing,mass_matrix=I) : Defines the RODE with the specified functions. The default noise is
f: The drift function in the SDE.
u0: The initial condition.
tspan: The timespan for the problem.
noise: The noise process applied to the noise upon generation. Defaults to Gaussian white noise. For information on defining different noise processes, see the noise process documentation page
noise_prototype: A prototype type instance for the noise vector. It defaults to
nothing, which means the problem should be interpreted as having a noise vector whose size matches
callback: A callback to be applied to every solver which uses the problem. Defaults to nothing.
mass_matrix: The mass-matrix. Defaults to