Support for SDE based models.

[vwiela]

It would be great to have the feature of a PEtabSDEProblem, where the model is not a ODe but a SDE.
Maybe for a start, supporting the conversion of a SBML model to an SDEProblem would be a good step.

[sebapersson]

This should be doable, especially when the model is provided as a Catalyst ReactionSystem, or if the model is provided via a SBML file. Moreover, the same parameter mapping structs which are used PEtabODEProblem can probably also be used.

The natural question is what functionality a PEtabSDEProblem should support. Currently the PEtabODEProblem contains functions for computing the likelihood, and its gradients. Now for a SDE computing the likelihood is seldom possible. So I was thinking the output should be easy to integrate with methods like ABC, and pseudo-marginal particle MCMC. So how about the PEtabSDEProblem containing functions for:

• Computing the observable for observed time-points
• Computing the SDE solution for a provided experimental condition
• Computing the SDE solution between two time-points (for particle filters).

Do you think anything additional would be needed?