Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity

In this paper we study a class of backward stochastic differential equations (BSDEs) of the form dY_t = −AY_t dt − f_0(t, Y_t )dt − f_1(t, Y_t , Z_t )dt + Z_t dW_t , 0≤ t ≤ T ; Y_T = ξ in an infinite dimensional Hilbert space H, where the unbounded operator A is sectorial and dissipative and the nonlinearity f_0(t, y) is dissipative and defined for y only taking values in a subspace of H. A typical example is provided by the so-called polynomial nonlinearities. Applications are given to stochastic partial differential equations and spin systems.