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A stochastic process is a collection of random variables usually indexed by a totally ordered set.

3 votes

If $\mathcal{F}_t$ is separable why is $\mathcal{F}_\infty$ generated by a random variable?

Yes, you can define separable by saying that it means "generated by a countable collection of (real) random variables", and you can always assume that all these variables take values in $[0,1]$. Then …
Thierry de la Rue's user avatar