TY - JOUR
T1 - A property of two-parameter martingales with path-independent variation
AU - Nualart, David
AU - Utzet, Frederic
PY - 1987/1/1
Y1 - 1987/1/1
N2 - 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.
AB - 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.
KW - path-independent variation
KW - quadratic variation
KW - two-parameter martingales
UR - https://www.scopus.com/pages/publications/45949121560
U2 - 10.1016/0304-4149(87)90026-3
DO - 10.1016/0304-4149(87)90026-3
M3 - Article
SN - 0304-4149
VL - 24
SP - 31
EP - 49
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
ER -