Also by analogy with continuous-time Markov processes, it might be easier to forget about individual trajectories and instead think about the “flow” of probability density in phase space which can probably be described by a partial differential equation without needing to define your own Riemann sums, path integrals and such. Or maybe I’m missing something here and you really need customized machinery?
It might work. I haven’t thought about it yet.
Also Cosma Shalizi is an expert on both causal models and continuous-time stochastic processes, so maybe you could ask him or look at his work if you haven’t seen it already.
I know of him and have read some of his stuff, but the work isn’t in a sufficiently stable state to bother an academic with it yet. I need more evidence that this is the fruitful path. I expect it would be difficult to convince him of the value of such an effort, since there’s no evidence yet that it’s even different from what is being done already.
It might work. I haven’t thought about it yet.
I know of him and have read some of his stuff, but the work isn’t in a sufficiently stable state to bother an academic with it yet. I need more evidence that this is the fruitful path. I expect it would be difficult to convince him of the value of such an effort, since there’s no evidence yet that it’s even different from what is being done already.