Ito's formula for two-parameter stochastic integrals with respect to martingale measures (Q760964)

The author derives the Ito's formula for a purely discontinuous two- parametric martingale \(\xi\) (t), which is a stochastic integral with respect to a martingale measure \(\mu\) : \[ \xi (t)=(\gamma *\mu)_ t=\iint_{[0,t]\times R}\gamma (s,u)\mu (ds,du). \] Here \(t=(t_ 1,t_ 2)\in R^ 2_+\), \([0,t]=[0,t_ 1]\times [0,t_ 2]\), \(\nu (ds,du)=\nu (\omega,ds,du)\) is a random integer-valued measure on \(R^ 2_+\times R\) satisfying some special conditions, \(\pi\) (ds,du) is a dual predictable projection of \(\nu\) and \(\mu =\nu -\pi\).