Gaussian Processes with Sample Paths in Reproducing Kernel Banach Spaces

The paper explores the relationship between Gaussian processes and Gaussian random elements within reproducing kernel Banach spaces. It demonstrates that the covariance operator of a weak second‑order Radon probability measure on such a space is uniquely defined by a symmetric positive‑definite function, and in the Gaussian case it identifies which functions correspond to covariance operators via γ‑radonifying operators. Leveraging these findings, the authors extend Driscoll’s theorem to the setting of reproducing kernel Banach spaces.

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