Related papers: Similarity Between Two Stochastic Differential Sys…
We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) S when the measures are indexed by another poset A. We give counterexamples…
This paper is concerned with a partially observed hybrid optimal control problem, where continuous dynamics and discrete events coexist and in particular, the continuous dynamics can be observed while the discrete events, described by a…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
We present a systematic expansion in the ratio between the level spacing and temperature and employ it to evaluate differences between statistical mechanics and thermodynamics in finite disordered systems. These differences are related to…
We prove a stochastic averaging theorem for stochastic differential equations in which the slow and the fast variables interact. The approximate Markov fast motion is a family of Markov process with generator ${\mathcal L}_x$ for which we…
We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases:…
The stochastic block model is a popular tool for detecting community structures in network data. Detecting the difference between two community structures is an important issue for stochastic block models. However, the two-sample test has…
Prediction error and maximum likelihood methods are powerful tools for identifying linear dynamical systems and, in particular, enable the joint estimation of model parameters and the Kalman filter used for state estimation. A key…
In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…
We demonstrate the phenomenon of stochastic resonance (SR) for discrete-time dynamical systems. We investigate various systems that are not necessarily bistable, but do have two well defined states, switching between which is aided by…
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex…
We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics…
The goal of this article is to study how combinatorial equivalence implies topological conjugacy. For that, we introduce the concept of kneading sequences for nonautonomous discrete dynamical systems and show that these sequences are a…
Data-driven techniques for analysis, modeling, and control of complex dynamical systems are on the uptake. Koopman theory provides the theoretical foundation for the popular kernel extended dynamic mode decomposition (kEDMD). In this work,…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
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…
The synchronization between two dynamical systems is one of the most appealing phenomena occurring in Nature. Already observed by Huygens in the case of two pendula, it is a current area of research in the case of chaotic systems, with…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…