Sample Path Regularity of Gaussian Processes from the Covariance Kernel

Understand

Gaussian processes (GPs) are the most common formalism for defining probability distributions over spaces of functions.

• While applications of GPs are myriad, a comprehensive understanding of GP sample paths, i.e.
• the function spaces over which they define a probability measure, is lacking.
• In practice, GPs are not constructed through a probability measure, but instead through a mean function and a covariance kernel.