So simulating a $nD$ Weiner process is easy enough, just generate points from a standard $nD$ Gaussian distribution and take the cumulative sum. If $n=1$, I know that such a Weiner process is just a Gaussian process with covariance function $\text{Cov}(X_s, X_t) = \min\{ s, t \}$. Can this somehow be generalized to higher dimensions? That is, is it possible to sample random curves in $\mathbb{R}^2$ using some sort of Gaussian process? Could you construct the mean function as some sort of parametric curve? Couldn't find anything about this after searching online, so I'm curious to hear your thoughts on this.
2026-03-31 05:40:00.1774935600
Gaussian process with scalar input and 2D output
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