  In this paper, on the sublinear expectation space, we establish a comparison
theorem between independent and convolutionary random vectors, which states
that the partial sums of those two sequences of random vectors are identically
distributed. Under the sublinear framework, through the comparison theorem,
several fundamental limit theorems for convolutionary random vectors are
obtained, including the law of large numbers, the central limit theorem and the
law of iterated logarithm.
