If probability laws govern the production of stochastic events, then can these events truly be called random? Because they do in fact occur within the bounds of expected possibility. The quality of ‘random’ undecidability is internally specific to the expected possibility range. So it arises as a function of the form of expectation. The randomness of probable events cannot be characterised entirely as anomaly.
The range of randomness is still determinate, a function of determinate expectation.
The philosophical issue or problem with Markov assumption, of determinate events without memories, would consist of several theoretical neglects. These neglects may not be considered significant, in terms of experimental or working criteria hinged on the practical production of useful physical processes, but it seems to me that the possibilities indicated by such neglects, could eventually take on increasing significance in future forms of scientific consideration.
The obvious neglect, is the quantum mechanical phenomenon of entanglement, and whatever future significances that might hold.
The next neglect, is the possible risk of allowing premature assumptions of discontinuity, merely because tangible, physical influences, cannot be found. Then going on to a dogmatics of absolute, anomalous emergence. This is not to suggest determinate, ‘hidden variables’, or some such. It’s just a caution not to absolutise anomaly. Such an absolutism risks all the insularity of outlook characterising any other absolutism.
The reason that this is so, is contingent on foundational assumptions of universal delimitation. If absolute boundaries cannot in principle be drawn, attributions of quality can only be tentative and contingent. Given various forms of infinity, working approximations are accessible or available, but those have far more to do with forms of apprehension and experiment, with expectations, then with any absolute knowledge of a hypothetical universal object whose ultimate parameters cannot be found.