# Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity

## TL;DR

This paper investigates a class of infinite-dimensional backward stochastic differential equations with dissipative operators and locally Lipschitz nonlinearities, providing theoretical results and applications to SPDEs and spin systems.

## Contribution

It introduces a framework for BSDEs with unbounded dissipative operators and locally Lipschitz nonlinearities, extending existing theory to more general infinite-dimensional settings.

## Key findings

- Existence and uniqueness results for the class of BSDEs studied.
- Application to stochastic partial differential equations.
- Application to spin systems.

## 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.