Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type: { tabular}{ rlll} $-dY_t$ &=& $f(t, Y_t, Z_t, Y_{ t+\delta(t)}, Z_{ t+\zeta(t)})dt-Z_tdB_t, $ & $ t\in[0, T];$ $Y_t$ &=& $\xi_t, $ & $t\in[T, T+K];$ $Z_t$ &=& $\eta_t, $ & $t\in[T, T+K].$ In this paper, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional anticipated backward stochastic differential equations with generators independent of the anticipated term of $Z$.
Categories: math.PR