Moduli of continuity for l az-valued Gaussian random fields

This paper establishes the general moduli of continuity for l (az)-valued Gaussian random fields {X(t):= (X (1)(t),X (2)(t), h.), t a [0, az) (N) } indexed by the N-dimensional parameter t:= (t (1),aEuro broken vertical bar,t (N) ), under the explicit condition yielding that the covariance function of distinct increments of X (k) (t) for fixed k a parts per thousand 1 is positive or nonpositive.