Gaussian Measures in $B_p$

Abstract

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.