Marco Fuhrman

Generalized Mehler Semigroups: The Non-Gaussian Case

We study generalized Mehler semigroups, introduced in [7], with special emphasis on the non-Gaussian case. We review and simplify the method of construction. In the general (non-Gaussian) case we construct an associated cadlag Markov process in an appropriate state space obtained as a solution of a stochastic equation which can be solved ‘ω by ω’. We also show tightness of the associated (r, p)-capacities. Invariant measures, time regularity and a definition of the generator are also studied.

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

Backward stochastic differential equation driven by a marked point process: An elementary approach with an application to optimal control.

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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

Smoothing properties of nonlinear stochastic equations in Hilbert spaces.

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Randomized and backward SDE representation for optimal control of non-Markovian SDEs

, with generator

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

. We then consider a backward stochastic differential equation depending on

Hypercontractivity properties of nonsymmetric ornstein-uhlenbeck semigroups in hilbert spaces

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