I've read that $$x_t = A\sin(t) + B\cos(t)$$ is a deterministic process, where $A,B \sim N(0,1)$ and independent, $t \in \mathbb N$.
How is it possible? At time $t$ we need to draw from two random variables!
Thanks!
2026-02-22 21:26:56.1771795616
$x_t = A\sin(t) + B\cos(t)$ is deterministic
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Page 5 of this document to which you linked in comments contains the answer to your question.
"Deterministic" as defined there does not mean "not random".
It means it can be predicted by using the entire past.
I would interpret that as follows: the conditional probability distribution of the future of the process, given the past of the process, assigns probability $1$ to a single path.
Thus if you see the path up to a certain time, you then know the realized values of those two random variables $A$ and $B$ and so you know the whole future of the process.