Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity

Fulvia Confortola

doi:10.1016/j.spa.2006.09.008

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arXiv · 0704.0509

Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity

Fulvia Confortola

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Abstract

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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BibTeX RIS

Fulvia Confortola. 2007-04-04. Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity. https://doi.org/10.1016/j.spa.2006.09.008

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