I'm reading this paper describing the capabilities of the ESA's DELTA space debris forecast model.

It's clear that this model uses a statistical, flux-based model derived from the MASTER debris collision risk assessment tool.

However, it's not immediately clear to me whether taking such a flux-based approach, rather than considering individual pieces of debris would qualify this as a stochastic one.

Are flux-based modelling techniques fundamentally stochastic?

  • $\begingroup$ Great question! I've managed to get through life not knowing what stochastic means exactly, and I have a hunch a good fraction of others would be able to say so as well. I have a hunch it has to do with (just for example) how they might or might not use a random number generator to initiate uncorrelated objects for the flux simulation, but I am not sure. Any chance you could add a simple definition to help answer authors who may know about space debris forecasting to better address the stochasticity issue? Thanks! $\endgroup$
    – uhoh
    May 14, 2023 at 22:48
  • $\begingroup$ What is "flux" in this context (probably not related to capacitors)? Transport flux? $\endgroup$ May 15, 2023 at 21:53

1 Answer 1


I think the question in your title and the question posed in your body might have different answers.

DELTA itself contains a stochastic process for collision prediction (see page 2) and so is inherently stochastic itself (though the authors prefer to call it "semi-deterministic"):

The final source of space debris in DELTA are collision events. The collision event prediction is done by using a target centered approach, developed to stochastically predict impacts between all objects within the DELTA population [7, 8, 9].

There's also a number of Monte Carlo steps, which are going to necessarily be stochastic (starting on page 3).

I've struggled some with the answer to the body question and I think that there is a way to make even a flux-based model completely non-stochastic if you don't have steps like the one I've quoted about collision events, where there's a sort of collapse from statistics to an event by "rolling the dice." If you kept the representation "in statistics" — i.e., a "collision" is some kind of convolution and now there's a spread of probabilities of debris fluxes and the ultimate result is also some set of statistics — then I think it might not be a stochastic process.

Hopefully that's enough hedging on that. I stand by DELTA itself being stochastic though.

  • 1
    $\begingroup$ This largely agrees with the conclusions I came to myself on this matter. Although your thoughts on the body-question are definitely more developed than mine were so thank you! $\endgroup$ May 15, 2023 at 9:36

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