Stochastic indistinguishability

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A property of two random processes and which states that the random set

can be disregarded, i.e. that the probability of the set is equal to zero. If and are stochastically indistinguishable, then for all , i.e. and are stochastically equivalent (cf. Stochastic equivalence). The opposite, generally speaking, is not true, but for processes that are continuous from the right (left), stochastic indistinguishability follows from stochastic equivalence.


[1] C. Dellacherie, "Capacités et processus stochastiques" , Springer (1972)



[a1] C. Dellacherie, P.A. Meyer, "Probabilities and potential" , A , North-Holland (1978) (Translated from French)
How to Cite This Entry:
Stochastic indistinguishability. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.N. Shiryaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article