Related papers: Invariant measure selection by noise: An Example
In the first part of the paper, we consider a discrete-time stochastic control system. We show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the…
Computation plays a key role in predicting and analyzing natural phenomena. There are two fundamental barriers to our ability to computationally understand the long-term behavior of a dynamical system that describes a natural process. The…
Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a…
This paper considers uncertainty quantification in systems perturbed by stochastic disturbances, in particular, Gaussian white noise. The main focus of this work is on describing the time evolution of statistical moments of certain…
We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to determine the minimal additive forcing…
One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with…
Given a dynamical system, a characteristic measure is a Borel probability measure invariant under all of its automorphisms. Frisch and Tamuz asked if every symbolic system supports such a measure. Motivated by this problem, we study the…
We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic…
We describe all boundedly finite measures which are invariant by Cartesian powers of an infinite measure preserving version of Chacon transformation. All such ergodic measures are products of so-called diagonal measures, which are measures…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
We are interested in viscous scalar conservation laws with a white-in-time but spatially correlated stochastic forcing. The equation is assumed to be one-dimensional and periodic in the space variable, and its flux function to be locally…
We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on the parameter…
The evolution of observable quantities of finite quantum systems is analyzed when the latter are subject to nondestructive measurements. The type and number of measurements characterize the level of decoherence produced in the system. A…
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
In this paper we study a class of \emph{self-consistent dynamical systems}, self-consistent in the sense that the discrete time dynamics is different in each step depending on current statistics. The general framework admits popular…
This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form,…
In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for the stability in probability of stochastic dynamical systems with symmetries and…
Reservoir computing systems are constructed using a driven dynamical system in which external inputs can alter the evolving states of a system. These paradigms are used in information processing, machine learning, and computation. A…
For the deterministic dyadic model of turbulence, there are examples of initial conditions in $l^2$ which have more than one solution. The aim of this paper is to prove that uniqueness, for all $l^2$-initial conditions, is restored when a…
Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…