In order to specify a stochastic process, is it sufficient to specify all the finite-dimensional distributions of the stochastic process? Can there exist two stochastic processes that agree in all the marginal distributions, but are not equal?
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1Sure, take two independent Brownian motions defined on the same probability space for example. But you first need to make your idea of "equal" precise. – Calculon Jul 04 '15 at 16:39
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I mean equal in distribution, but I am not sure if that is the correct term to use? – user2808118 Jul 04 '15 at 16:43
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What about the reply to the first question? – user2808118 Jul 04 '15 at 16:45