Gianmario Tessitore

Existence, uniqueness and space regularity of the adapted solutions of a backward spde

The existence and uniqueness of an adapted solution is proved, under very general assumptions on the coefficients, for a linear, infinite dimensional, stochastic differential equation with final time condition. Moreover the attention is focused on the regularity “in space” of this Solutions

Ergodic BSDEs and Optimal Ergodic Control in Banach Spaces

In this paper we introduce a new kind of backward stochastic differential equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness, and regularity of solution to ergodic BSDEs. Then we apply these results to the optimal ergodic control of a Banach valued stochastic state equation. We also establish the link between the ergodic BSDEs and the associated Hamilton-Jacobi-Bellman equation. Applications are given to the optimal ergodic control of stochastic partial differential equations.

Stochastic Equations with Delay: Optimal Control via BSDEs and Regular Solutions of Hamilton-Jacobi-Bellman Equations

We consider an Ito stochastic differential equation with delay, driven by Brownian motion, whose solution, by an appropriate reformulation, defines a Markov process

Some remarks on the Riccati equation arising in an optimal control problem with state- and control-dependent noise

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Existence of Optimal Stochastic Controls and Global Solutions of Forward-Backward Stochastic Differential Equations

with values in a space of continuous functions

On a Class of Stochastic Optimal Control Problems Related to BSDEs with Quadratic Growth

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Stochastic maximum principle for optimal control of SPDEs

, with generator

On the Backward Stochastic Riccati Equation in Infinite Dimensions

\mathcal{L}

Controlled Stochastic Differential Equations under Constraints in Infinite Dimensional Spaces

. We then consider a backward stochastic differential equation depending on

Ergodic Control of Infinite Dimensional SDEs with Degenerate Noise

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