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 d Y t = − A Y t d t − f 0 ( t , Y t ) d t − f 1 ( t , Y t , Z t ) d t + Z t d W 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.