In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics, which describes the boundary conditions of the internal system. In other terms, we are… (More)
In this paper we study one dimensional backward stochastic differential equations (BSDEs) with random terminal time not necessarily bounded or finite when the generator F (t, Y, Z) has a quadratic growth in Z. We provide existence and uniqueness of a bounded solution of such BSDEs and, in the case of infinite horizon, regular dependence on parameters. The… (More)
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−f 0 (t, Y t)dt−f 1 (t, Y t , Z t)dt+Z t dW t , 0 ≤ t ≤ T ; Y T = ξ in an infinite dimensional Hilbert space H, where the unbounded operator A is… (More)
The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic optimal control.