We know that in mathematics there are some propositions which, given a set of axioms, are undecidable; and other propositions which, for what we know, might be undecidable. Are there example of these two categories in probability theory? My guess would be yes, given the set-theoretic foundations of the theory, but I could not find any concrete example. Thank you in advance for your attention.
Are there indecidable problems in probability?
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1A google search reveals the following papers: (1) Gamarnik, David. "On deciding stability of constrained homogeneous random walks and queueing systems." *Mathematics of Operations Research* 27.2 (2002): 272-293. (2) Gamarnik, David. "On the undecidability of computing stationary distributions and large deviation rates for constrained random walks." *Mathematics of Operations Research* 32.2 (2007): 257-265. – 2017-01-01