A stochastic Taylor formula for functionals of two-parameter semimartingales (Q908583)

Consider a two-parameter semimartingale of the form \[ X_ z=\int_{R_ z}q dw+\iint_{R_ z\otimes R_ z}T dw dw+\iint_{R_ z\otimes R_ z}\alpha d\lambda dw+\iint_{R_ z\otimes R_ z}\beta dwd\lambda +\int_{R_ z}b d\lambda \] where W is a two-parameter Wiener process, and \(\lambda\) is the Lebesgue measure on the plane. The main result of the paper is a stochastic Taylor formula which represents a decomposition of the increments \(F(X_ z)-F(X_ 0)\) of sufficiently smooth functions F into a finite sum of multiple stochastic integrals with constant integrands depending on \(X_ 0\) and a remainder which is a finite sum of other multiple stochastic integrals with integrands depending on \(X_{z_ I}\), \(z_ I\in R_ z\). The integrators in this expansion are also semimartingales determined by X. Some estimates of the remainder are obtained.