AN Lp ‘COUSIN OF COBOUNDARY’ THEOREM FOR RANDOM FIELDS

Abstract

AbstractIt is known that for a given $p\in [1,\infty )$ and a given strictly stationary sequence of random variables, the p-norms of the partial sums are bounded if and only if the sequence consists of successive differences from another strictly stationary sequence with finite p-norm. Here this is generalized to random fields, and the assumption of stationarity is relaxed. The index $p= \infty $ is included.