The paper derives conditions under which the increments of a vector process are associated-i.e. under which all pairs of increasing functions of the increments are positively correlated. The process itself is associated if it is generated by a family of associated and monotone kernels. The paper shows that the increments are associated if the kernels are associated and, in a suitable sense, convex. In the Markov case, it notes a connection between associated increments and temporal stochastic convexity. The present analysis is motivated by a question in variance reduction: assuming that a normalized process and its normalized compensator converge to the same value, which is the better estimator of that limit? Under some additional hypotheses the paper shows that, for processes with conditionally associated increments, the compensator has smaller asymptotic variance.
