Related papers: On time-inhomogeneous controlled diffusion process…
The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the…
We study Lorentz processes in two different settings. Both cases are characterized by infinite expectation of the free-flight times, contrary to what happens in the classical Gallavotti-Spohn models. Under a suitable Boltzmann-Grad type…
For a two by two reaction-diffusion system on a bounded domain we give a simultaneous stability result for one coefficient and for the initial conditions. The key ingredient is a global Carleman-type estimate with a single observation…
In this paper, we study the regularity of the value function associated with a stochastic control problem where two controls act simultaneously on a modulated multidimensional diffusion process. The first is a switching control modelling a…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…
In this article, we study the existence of insensitizing controls for a nonlinear reaction-diffusion equation with dynamic boundary conditions. Here, we have a partially unknown data of the system, and the problem consists in finding…
An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
We consider a non homogeneous Gompertz diffusion process whose parameters are modified by generally time-dependent exogenous factors included in the infinitesimal moments. The proposed model is able to describe tumor dynamics under the…
The main result in this paper is a variational formula for the exit rate from a bounded domain for a diffusion process in terms of the stationary law of the diffusion constrained to remain in this domain forever. Related results on the…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
We consider a general class of stochastic optimal control problems, where the state process lives in a real separable Hilbert space and is driven by a cylindrical Brownian motion and a Poisson random measure; no special structure is imposed…
The sensitivity properties of intermittent control are analysed and the conditions for a limit cycle derived theoretically and verified by simulation.
This paper is a survey on some recent aspects and developments in stochastic control. We discuss the two main historical approaches, Bellman's optimality principle and Pontryagin's maximum principle, and their modern exposition with…
We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a…
We present the concept of time-domain bound states in continuum. We show that a rapid judiciously-designed temporal modulation of the refractive index in a spatially homogenous medium gives rise to a bound state in time embedded in a…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
Two finite-time consensus protocols are proposed for multi-dimensional multi-agent systems, using direction-preserving and component-wise signum controls respectively. Filippov solutions and non-smooth analysis techniques are adopted to…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…