Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity

Details Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity

2007-04-04

arxiv.org/abs/0704.0509v1

Stochastic Processes and their Applications 117 (2007) 613-628

Mathematics

Probability

22 pages

Scientific paper

10.1016/j.spa.2006.09.008

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) 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 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.

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