Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity

AbstractIn this paper we study a class of backward stochastic differential equations (BSDEs) of the form dYt=−AYtdt−f0(t,Yt)dt−f1(t,Yt,Zt)dt+ZtdWt,0≤t≤T;YT=ξ in an infinite dimensional Hilbert space H, where the unbounded operator A is sectorial and dissipative and the nonlinearity f0(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