Related papers: Dynamically defined measures and equilibrium state…
I show that a class of Linear DSGE models with one endogenous state variable can be represented as a three-state Markov chain. I develop a new analytical solution method based on this representation, which amounts to solving for a vector of…
Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on {\em analytically-solvable}…
Abstractions of dynamical systems enable their verification and the design of feedback controllers using simpler, usually discrete, models. In this paper, we propose a data-driven abstraction mechanism based on a novel metric between Markov…
Discrete time random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniform continuous and contractive are considered. A notion of a…
For any $C^1$ diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy, a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms of the…
We obtain some results of existence and continuity of physical measures through equilibrium states and apply these to non-uniformly expanding transformations on compact manifolds with non-flat critical sets, obtaining sufficient conditions…
Symmetry properties of stochastic dynamical systems described by stochastic differential equation of Stratonovich type and related conserved quantities are discussed, extending previous results by Misawa. New conserved quantities are given…
Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using…
These notes give a summary of techniques used in large deviation theory to study the fluctuations of time-additive quantities, called dynamical observables, defined in the context of Langevin-type equations, which model equilibrium and…
We consider the boundary driven harmonic model, i.e. the Markov process associated to the open integrable XXX chain with non-compact spins. Using the factorial moments we characterize the stationary measure as a mixture of product measures.…
New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…
We show that intensive thermodynamic parameters associated to additive conserved quantities can be naturally defined from a statistical approach in far-from-equilibrium steady-state systems, under few assumptions, and without any detailed…
The behavior of dynamical system interacting with non-equilibrium medium is investigated. Formally exact kinetic equations are derived for the statistical operator of the dynamical system and the macroscopic parameters of the medium. In the…
Distance measures are indispensable tools in quantum information processing and quantum computing. This since they can be used to quantify to what extent information is preserved, or altered, by quantum processes. In this paper we propose a…
An extension of the idea of state tameness is presented in a dynamic framework. The proposed model for financial markets is rich enough to provide analytical tools that are mostly obtained in models that arise as the solution of SDEs with…
This paper is partly an exposition, and partly an extension of our work [1] to the multiparameter case. We consider certain classes of parametrized dynamically defined measures. These are push-forwards, under the natural projection, of…
We give several new characterizations of Caratheodory convergence of simply connected domains. We then investigate how different definitions of convergence generalize to the multiply-connected case.
Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between…
We describe a method, using periodic points and determinants, for giving alternative expressions for dynamical quantities (including Lyapunov exponents and Hausdorff dimension of invariant sets) associated to analytic hyperbolic systems.…
In this paper, we establish an iterative data-driven approach to derive guaranteed bounds on nonlinearity measures of unknown nonlinear systems. In this context, nonlinearity measures quantify the strength of the nonlinearity of a dynamical…