For $p \geq 1$, conditions for a separable Gaussian process to have sample paths of finite $p$-variation are given in terms of the mean function and the covariance function. A process with paths of finite $p$-variation may or may not induce a tight measure on the nonseparable Banach space $B_p$. Consequences of tightness and conditions for tightness are given.
Naresh C. Jain. Ditlev Monrad. "Gaussian Measures in $B_p$." Ann. Probab. 11 (1) 46 - 57, February, 1983. https://doi.org/10.1214/aop/1176993659