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Jan 15, 2020 at 19:15 comment added user113782 I agree, it very much depends on one's mindset. I was working on this particular aspect of the theory when I bumped into the question.
Jan 15, 2020 at 9:22 comment added S.Surace @encore Thanks for the comment. Upon re-reading the question and my answer over two years later, I think I indeed misread 'the same' as 'have the same distribution'. Your answer makes sense and fully clarifies the situation.
Jan 13, 2020 at 10:35 comment added user113782 You appear to be confusing indistinguishability of processes with their distributional properties. The same random variable will have different distributions under different equivalent measures. Does not change the fact that it is the same r.v.
Dec 4, 2017 at 22:10 history answered S.Surace CC BY-SA 3.0