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[umbralcalc]

• multidimensional drift diffusion with arbitrary time dependence and coupling of the coefficients plus integrators which work with jumps (implicit Euler?)
• multidimensional Jump terms which can be time dependent, compound poisson, cox processes, hawkes processes, q-hawkes processes, mutually self-exciting processes

[umbralcalc]

the general idea I guess is to be able to simulate stochastic trajectories on either discrete or continuous state spaces... for continuous we would have, quite generally dx(t) = (time-continuous functions) (x(t-dt), x(t-2dt), ..., t)

• (time-continuous noises) (x(t-dt), x(t-2dt), ..., t)
• (jump noises) (x(t-dt), x(t-2dt), ..., t) where x(t) is a continuous state variable matrix (e.g., index-0 for dimensions of the process at each node of a network and index-1 for each of the nodes) in time - note that this can also be extended to discrete state transition models by replacing x(t) -> p(t) where p(t) is the matrix of probabilities for the process to be in each of the states (encoded by the index used for dimensions when it was x(t))