A Random Access Protocol Approach to Stochastic Jumping Systems with Singular Perturbations

Singular perturbations to semilinear stochastic heat equations

We consider a class of singular perturbations to the stochastic heat equation or semilinear variations thereof. The interesting feature of these perturbations is that, as the small parameter ε tends to zero, their solutions converge to the ‘wrong’ limit, i.e. they do not converge to the solution obtained by simply setting ε = 0. A similar effect is also observed for some (formally) small stocha...

Stochastic perturbations to dynamical systems: a response theory approach

We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory. We find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the case of additive and multiplicative noise. We also show that the difference between the expectation value of...

Integral approach to sensitive singular perturbations

We consider singular perturbation elliptic problems depending on a parameter ε such that, for ε = 0 the boundary conditions are not adapted to the equation (they do not satisfy the Shapiro Lopatinskii condition). The limit only holds in very abstract spaces out of distribution theory involving complexification and non-local phenomena. We give a very elementary model problem showing the main fea...

A delay-dependent approach to H∞ filtering for stochastic delayed jumping systems with sensor non-linearities

In this paper, a delay-dependent approach is developed to deal with the stochastic H∞ filtering problem for a class of Itô type stochastic time-delay jumping systems subject to both the sensor nonlinearities and the exogenous nonlinear disturbances. The time delays enter into the system states, the sensor nonlinearities and the external nonlinear disturbances. The purpose of the addressed filte...

A new Approach to the Multi-Objective Control of Linear Singular Perturbation Systems