RODE Problems

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:

\[\frac{du}{dt} = f(t,u,W(t))\]

where W(t) is a random process. f should be specified as f(t,u,W) (or in-place as f(t,u,W,du)), and 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.

Constructors

RODEProblem{isinplace}(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 WHITE_NOISE. isinplace optionally sets whether the function is inplace or not. This is determined automatically, but not inferred.

Fields

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 u0.
callback: A callback to be applied to every solver which uses the problem. Defaults to nothing.
mass_matrix: The mass-matrix. Defaults to I, the UniformScaling identity matrix.