I came across the phrase "let $G_t$ be a Gaussian process conditioned to be positive".
My literal interpretation of this from English is that $G_t$ is a Gaussian process such that $G_t>0$ for each $t$. But I am also aware of the definition of the conditional expectation of a random variable with respect to a $\sigma$-algebra, although I have not seen what is meant by a a stochastic process conditioned to possess some property $P$.
Can someone clarify what is the precise meaning of "let $G_t$ be a Gaussian process conditioned to be positive"?