Related papers: On the gap between deterministic and probabilistic…
We consider a finite family of invertible $2 \times 2$ real matrices and a transitive Markov shift on the index set. Let $\lambda$ be the top Lyapunov exponent for random matrix products driven by the Markov shift. We prove that, if the…
This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state…
In this short paper, we consider discrete-time Markov chains on lattices as approximations to continuous-time diffusion processes. The approximations can be interpreted as finite difference schemes for the generator of the process. We…
We propose to model the records of the maximum Drawdown in capital markets by means a Piecewise Deterministic Markov Process (PDMP). We derive statistical results such as the mean and variance that describes the sequence of maximum Drawdown…
This paper studies the exponential stability of random matrix products driven by a general (possibly unbounded) state space Markov chain. It is a cornerstone in the analysis of stochastic algorithms in machine learning (e.g. for parameter…
We present a general formalism for computing the largest Lyapunov exponent and its fluctuations in spatially extended systems described by diffusive fluctuating hydrodynamics, thus extending the concepts of dynamical system theory to a…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed…
This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing…
We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state…
We introduce a new approach to evaluate the largest Lyapunov exponent of a family of nonnegative matrices. The method is based on using special positive homogeneous functionals on $R^{d}_+,$ which gives iterative lower and upper bounds for…
In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…
Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
We study the singular values and Lyapunov exponents of non-stationary random matrix products subject to small, absolutely continuous, additive noise. Consider a fixed sequence of matrices of bounded norm. Independently perturb the matrices…
We decide the stability and compute the Lyapunov exponent of continuous-time linear switching systems with a guaranteed dwell time. The main result asserts that the discretization method with step size~$h$ approximates the Lyapunov exponent…
For non-autonomous linear stochastic differential equations (SDEs), we establish that the top Lyapunov exponent is continuous if the coefficients "almost" uniformly converge. For autonomous SDEs, assuming the existence of invariant measures…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
The time it takes the fastest searcher out of $N\gg1$ searchers to find a target determines the timescale of many physical, chemical, and biological processes. This time is called an extreme first passage time (FPT) and is typically much…
Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical…