Related papers: Yet Another Quantitative Harris Theorem
We present a new sufficient condition for finite-gain $L_2$ input-to-output stability of a networked system. The condition requires a matrix, that combines information on the $L_2$ gains of the sub-systems and their interconnections, to be…
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning", to study their stable convergence…
This paper provides a Lyapunov-based small-gain theorem for input-to-state stability (ISS) of networks composed of infinitely many finite-dimensional systems. We model these networks on infinite-dimensional $\ell_{\infty}$-type spaces. A…
Learned models and policies can generalize effectively when evaluated within the distribution of the training data, but can produce unpredictable and erroneous outputs on out-of-distribution inputs. In order to avoid distribution shift when…
We propose a two step strategy for estimating one-dimensional dynamical parameters of a quantum Markov chain, which involves quantum post-processing the output using a coherent quantum absorber and a "pattern counting'' estimator computed…
Despite the exponential overhead to describe general multi-qubit quantum states and processes, efficient methods for certain state families and operations have been developed and utilised. The stabilizer formalism and the Gottesman-Knill…
In this article, we fill a gap in the literature regarding quantitative functional central limit theorems (qfCLT) for Hawkes processes by providing an upper bound for the convergence of a nearly unstable Hawkes process toward a…
This article deals with the implementation of the Smith Predictor for state feedback control in state space representation. The desired control law, obtained using partial differential equations and backstepping control, contains an…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give…
We introduce a definition of pressure for almost-additive sequences of continuous functions defined over (non-compact) countable Markov shifts. The variational principle is proved. Under certain assumptions we prove the existence of Gibbs…
This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…
The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…
A natural formulation of the theory of quantum measurements in continuous time is based on quantum stochastic differential equations (Hudson-Parthasarathy equations). However, such a theory was developed only in the case of…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
A comparison theorem for state-dependent regime-switching diffusion processes is established, which enables us to control pathwisely the evolution of the state-dependent switching component simply by Markov chains. Moreover, a sharp…
We derive the form of the Belavkin-Kushner-Stratonovich equation describing the filtering of a continuous observed quantum system via non-demolition measurements when the statistics of the input field used for the indirect measurement are…
We consider kinetic SDEs with low regularity coefficients in the setting recently introduced in [6]. For the solutions to such equations, we first prove a Harnack inequality. Using the abstract approach of [5], this inequality then allows…