Let M be a continuous two-parameter L4-martingale, vanishing on the axes, and f a C-function. In Itô's formula for f(M2) a new martingale M̃ is involved. This martingale can be interpreted formally as the stochastic integral ∫∂1M∂2M and it coincides with the martingale JM introduced by Cairoli and Walsh when M is strong. In this paper we prove that if M has path-independent variation, then M and M̃ are orthogonal. Also. we give some counter-examples to the reciprocal implication. © 1987.
|Journal||Stochastic Processes and their Applications|
|Publication status||Published - 1 Jan 1987|
- path-independent variation
- quadratic variation
- two-parameter martingales