The pathwise uniqueness of solution of non-Markovian stochastic differential equations with jumps in plane (Q1344605)

We consider the following non-Markovian stochastic differential equation with jumps in the plane \[ \begin{cases} dX_ z = \alpha (z,X) dB_ z + \beta (z,X) dz + \gamma (z,X) dN_ z, \quad z \in \mathbb{R}^ 2_ +,\\ X |_{\partial \mathbb{R}^ 2_ +} = x, \end{cases} \] where \(B\) is the two-parameter Brownian sheet, \(N\) is a compensated Poisson process and \(x\) is a process which is cadlag on \(\partial \mathbb{R}^ 2_ +\). A sufficient condition for the pathwise uniqueness of solutions of the above SDE is provided which is weaker than usual Lipschitz condition.