Related papers: A weak characterization of slow variables in stoch…
We propose a new geometric approach to describe the qualitative dynamics of chemical reactions networks. By this method we identify metastable regimes, defined as low dimensional regions of the phase space close to which the dynamics is…
Mean-field models are a popular tool in a variety of fields. They provide an understanding of the impact of interactions among a large number of particles or people or other "self-interested agents", and are an increasingly popular tool in…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
We propose matrix commutator based stability characterization for discrete-time switched linear systems under restricted switching. Given an admissible minimum dwell time, we identify sufficient conditions on subsystems such that a switched…
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…
We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
A perturbation framework is developed to analyze metastable behavior in stochastic processes with random internal and external states. The process is assumed to be under weak noise conditions, and the case where the deterministic limit is…
Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and…
In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…
The paper deals with a question of robustness of inferences, carried out on a continuous-time stationary process contaminated by a small trend, to this departure from stationarity. We show that a smoothed periodogram approach to parameter…
This paper addresses distributed parameter estimation in stochastic dynamic systems with quantized measurements, constrained by quantized communication and Markovian switching directed topologies. To enable accurate recovery of the original…
The graph-related symmetries of a reaction network give rise to certain special equilibria (such as complex balanced equilibria) in deterministic models of dynamics of the reaction network. Correspondingly, in the stochastic setting, when…
Many applications of contemporary science involve multiscale dynamics, which are typically characterized by the time and space scale separation of patterns of motion, with fewer slowly evolving variables and much larger set of faster…
In many applications, the common assumption that a driving noise process affecting a system is independent or Markovian may not be realistic, but the noise process may be assumed to be stationary. To study such problems, this paper…
We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the…
Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in…