Related papers: Dynamical systems with heavy-tailed random paramet…
We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to trajectories that stay within a bounded domain for asymptotically long times. This is motivated by the desire to characterize local dynamical…
Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…
We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional queue-length process. The tail…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
We consider the problem of probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities.…
This paper studies a continuous-time joint sampling-and-preemption problem, incorporating sampling and preemption penalties under general service-time distributions. We formulate the system as an impulse-controlled piecewise-deterministic…
Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced…
In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
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…
We consider linear dynamical systems with a structure of a multigraph. The vertices are associated to linear spaces and the edges correspond to linear maps between those spaces. We analyse the asymptotic growth of trajectories (associated…
In this paper, we investigate and develop a new approach to the numerical analysis and characterization of random fluctuations with heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare…
Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…
Markov decision processes (MDPs) are a fundamental model in sequential decision making. Robust MDPs (RMDPs) extend this framework by allowing uncertainty in transition probabilities and optimizing against the worst-case realization of that…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…
We classify the possible behaviors of a class of one-dimensional stochastic recurrent growth models. In our main result, we obtain nearly optimal bounds for the tail of hitting times of some compact sets. If the process is an aperiodic…
The collective properties of small material systems considered as semidynamical systems revealing the Markov-type irreversible evolution, are investigated. It is shown that these material systems admit their treatment as thermodynamic…