Related papers: Invariant Measures for Hybrid Stochastic Systems

We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…

Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…

We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…

In an effort to aid communication among different fields and perhaps facilitate progress on problems common to all of them, this article discusses hidden Markov processes from several viewpoints, especially that of symbolic dynamics, where…

One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…

We consider a discrete-time temporally-homogeneous conservative Markov process. We show that extremality of reversible measure implies extremality of invariant measure. Using analogue of Dirichlet form, we modify a proof that in stochastic…

We study invariant ergodic measures for quasiperiodically forced circle homeomorphisms and derive that either the system is uniquely ergodic or any such measure is associated to some invariant multigraph.

The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…

We consider Glauber-type stochastic dynamics of continuous systems \cite{BCC02}, \cite{KL03}, a particular case of spatial birth-and-death processes. The dynamics is defined by a Markov generator in such a way that Gibbs measures of Ruelle…

Quantum trajectories are Markov processes that describe the time-evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they are defined as solutions of the so-called "Stochastic Schr\"odinger Equations",…

We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…

We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly…

Stochastic hybrid systems are dynamic systems that undergo both random continuous-time flows and random discrete jumps. Depending on how randomness is introduced into the continuous dynamics, discrete transitions, or both, stochastic hybrid…

We consider the averaging principle for deterministic or stochastic systems with a fast stochastic component (family of continuous-time Markov chains depending on the state of the system as a parameter). We show that, due to bifurcations in…

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…

Modeling event dynamics is central to many disciplines. Patterns in observed event arrival times are commonly modeled using point processes. Such event arrival data often exhibits self-exciting, heterogeneous and sporadic trends, which is…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…

This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partition-based invariance…

There is studied an invariant measure structure of a class of ergodicl discrete dynamical systems by means of the measure generating function method