The continuity of the quadratic variation of two-parameter martingales

AbstractIt has been known that any L log+L-integrable two-parameter martingale M possesses a quadratic variation [M]. We show that the continuity properties of M are inherited by its quadratic variation. If M has no point jumps, [M] has no point jumps. [M] has at most axial jumps with respect to one of the coordinate axes in parameter space if M possesses this property. Finally, [M] is continuous along with M