Distribution of Gaussian Process Arc Lengths

摘要: We present the first treatment of arc length Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path is crucial quantity interest. Previously, only paths in one dimension have been considered, no theoretical consideration higher dimensional problems. fill gap existing literature by deriving moments stationary GP multiple dimensions. A new method to derive mean one-dimensional over finite interval, considering distribution integrand. This technique an approximate vector valued $\mathbb{R}^n$ moment matching distribution. Numerical simulations confirm our derivations.