Let R(s, t) be a continuous, nonnegative, real valued function on a <= s <= t <= b. Suppose [not partial differential]R/[not partial differential]s >= 0, [not partial differential]R/[not partial differential]t <= 0, and [not partial differential]2R/[not partial differential]t [not partial differential]t <= 0 in the interior of the domain. Then the extension of R to a symmetric function on [a, b] - [a, b] is a covariance function. Such a covariance is called biconvex. Let X(t) be a Gaussian process with mean 0 and biconvex covariance. X has a representation as a sum of simple moving averages of white noises on the line and plane. The germ field of X at every point t is generated by X(t) alone. X is locally nondeterministic. Under an additional assumption involving the partial derivatives of R near the diagonal, the local time of the sample function exists and is jointly continuous almost surely, so that the sample function is nowhere differentiable.
