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:

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

where W(t) is a random process. f should be specified as f(u,p,t,W) (or in-place as f(du,u,p,t,W)), 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(f::RODEFunction,u0,tspan,p=NullParameters();noise=WHITE_NOISE,rand_prototype=nothing,callback=nothing)
• RODEProblem{isinplace}(f,u0,tspan,p=NullParameters();noise=WHITE_NOISE,rand_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.

Parameters are optional, and if not given then a NullParameters() singleton will be used which will throw nice errors if you try to index non-existent parameters. Any extra keyword arguments are passed on to the solvers. For example, if you set a callback in the problem, then that callback will be added in every solve call.

For specifying Jacobians and mass matrices, see the DiffEqFunctions page.

Fields

• f: The drift function in the SDE.
• u0: The initial condition.
• tspan: The timespan for the problem.
• p: The optional parameters for the problem. Defaults to NullParameters.
• 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
• rand_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.
• kwargs: The keyword arguments passed onto the solves.