Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity
Abstract
In this paper we study a class of backward stochastic differential equations (BSDEs) of the form dY(t)= -AY(t)dt -f0(t,Y(t))dt -f1(t,Y(t),Z(t))dt + Z(t)dW(t) on the interval [0,T], with given final condition at time T, in an infinite dimensional Hilbert space H. 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.
0