Stefano Bonaccorsi

Stochastic partial differential equations with Dirichlet white-noise boundary conditions

Abstract The paper is devoted to one-dimensional nonlinear stochastic partial differential equations of parabolic type with non homogeneous Dirichlet boundary conditions of white-noise type. We formulate a set of conditions that a random field must satisfy to solve the equation. We show that a unique solution exists and that we can write it in terms of the stochastic kernel related to the problem. This formulation allows us to study the basic properties of the solution, as the continuity and the boundary-layer behavior, by means of Malliavin calculus.

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

\nu

STABILITY FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH DIRICHLET WHITE-NOISE BOUNDARY CONDITIONS

associated with the transition semigroup

A Semigroup Approach to Stochastic Dynamical Boundary Value Problems

P_t

Epidemic Outbreaks in Networks with Equitable or Almost-Equitable Partitions

; further, we identify its infinitesimal generator in the space

Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels

L^2(H;\nu)

A Stochastic Parabolic Equation with Nonlinear Flux on the Boundary Driven by a Gaussian Noise

.

Asymptotic Behavior of a Class of Nonlinear Stochastic Heat Equations with Memory Effects

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.

Volterra Equations Perturbed by a Gaussian Noise

In this paper we study the long-time behaviour a stochastic parabolic equation perturbed through the boundary; the perturbation is represented by a nonhomogeneous Dirichlet boundary condition of white-noise type. The existence of the solution for an equation of this kind was the object of a previous paper of the same authors. The estimates proved therein allow to study the asymptotic properties of the solution; we show that there exists a unique invariant measure that is exponentially mean square stable.