Abstract. We study continuity and moduli of continuity sample path properties of $\ell ^p$-valued Gaussian processes in general, and those of $\ell ^p$-valued Ornstein--Uhlenbeck processes in particular, for $1\leq p \leq2$.

AMS Subject Classification (1991): 60G15, 60G10, 60G17, 60F15; 60G07, 60F10

Keyword(s): Banach space valued processes, \ell ^p, -valued Gaussian processes, \ell ^p, -valued Ornstein--Uhlenbeck processes, moduli of continuity, quasi-increasing functions

Received June 15, 1994. (Registered under 5624/2009.)