Elisa Mastrogiacomo

ANALYSIS OF THE STOCHASTIC FITZHUGH–NAGUMO SYSTEM

In this paper we study a system of stochastic differential equations with dissipative nonlinearity which arise in certain neurobiology models. Besides proving existence, uniqueness and continuous dependence on the initial datum, we shall be mainly concerned with the asymptotic behaviour of the solution. We prove the existence of an invariant ergodic measure

Optimal control of stochastic differential equations with dynamical boundary conditions

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Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels

associated with the transition semigroup

Portfolio Optimization with Quasiconvex Risk Measures

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Portfolio Choice Under Cumulative Prospect Theory: Sensitivity Analysis and an Empirical Study

; further, we identify its infinitesimal generator in the space

Small noise asymptotic expansions for stochastic PDE's, I. The case of a dissipative polynomially bounded nonlinearity

L^2(H;\nu)

Small noise asymptotic expansions for stochastic PDE’s driven by dissipative nonlinearity and Lévy noise

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Invariant measures for stochastic differential equations on networks

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problems with nonstandard 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 concerned with nonstandard boundary conditions, as the value at the boundary is governed by a different stochastic differential equation.

An analytic approach to stochastic Volterra equations with completely monotone kernels

In this paper, we study a class of optimal control problems for stochastic Volterra equations in infinite dimensions. We are concerned with a class of stochastic Volterra integro-differential problem with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We provide a semigroup setting for the problem, by the state space setting; the applications to optimal control provide other interesting results and require a precise description of the properties of the generated semigroup. In our stochastic optimal control problems, the drift term of the equation has a linear growth in the control variable, the cost functional has a quadratic growth, and the control process belongs to the class of square integrable, adapted processes with no bound assumed on it. Our main results are the existence for the optimal feedback control, the identification of the optimal cost with the value

A Class of Lévy Driven SDEs and their Explicit Invariant Measures

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