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Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
We study random perturbations of multidimensional piecewise expanding maps. We characterize absolutely continuous stationary measures (acsm) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of…
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
Strong laws of large numbers are established for random fields with weak or strong dependence. These limit theorems are applicable to random fields with heavy-tailed distributions including fractional stable random fields. The conditions…
We revisit the concept of marginal stability in glasses, and determine its range of applicability in the context of avalanche-type response to slow external driving. We argue that there is an intimate connection between a pseudo-gap in the…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
Dilatively stable processes generalize the class of infinitely divisible self-similar processes. We reformulate and extend the definition of dilative stability introduced by Igl\'oi (2008) using characteristic functions. We also generalize…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
This paper is concerned with the problem of distributed estimation for time-varying interconnected dynamic systems with arbitrary coupling structures. To guarantee the robustness of the designed estimators, novel distributed stability…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
We present several new phenomena about almost sure convergence on homogeneous chaoses that include Gaussian Wiener chaos and homogeneous sums in independent random variables. Concretely, we establish the fact that almost sure convergence on…
Stable distributions are a celebrated class of probability laws used in various fields. The $\alpha$-stable process, and its exponentially tempered counterpart, the Classical Tempered Stable (CTS) process, are also prominent examples of…
?In this work, we study the orbital stability of stationary solutions to the relativistic Vlasov-Manev system. This system is a kinetic model describing the evolution of a stellar system subject to its own gravity with some relativistic…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
Defining administrative workflow events as a nonlinear dynamics that assume a random ordered or disordered growth rate of information processing, a method has been proposed for large-scale administrative systems that structures hybrid…
We define the notion of stochastic stability, already present in the literature in the context of smooth dynamical systems, for invariant measures of cellular automata perturbed by a random noise, and the notion of strongly stochastically…