The continuity of the quadratic variation of two-parameter martingales

Nikos E. Frangos and Peter Imkeller

Stochastic Processes and their Applications, 1988, vol. 29, issue 2, 267-279

Abstract: It 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.

Keywords: two-parameter; martingales; quadratic; variation; point; jumps; axial; jumps; continuity (search for similar items in EconPapers)
Date: 1988
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