If we have a Ornstein-Uhlenbeck process $X_t$ and $Y_t=\int_0^t X_s ds $, is $Y_t$ also a Gaussian process? is that true for any Gaussian process $X_t$? I know $Y_t$ is a Gaussian random variable for every $t$, but I want to know how to show the finite joint distribution is multivariate normal distribution.
2026-03-29 20:50:07.1774817407
is time integral of gaussian process a gaussian process?
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