相关论文: Yet Another Quantitative Harris Theorem

In this paper, we introduce a slight variation of the Dominated Coupling From the Past algorithm (DCFTP) of Kendall, for bounded Markov chains. It is based on the control of a (typically non-monotonic) stochastic recursion by a (typically…

In this paper we focus on a general type of mean-field stochastic control problem with partial observation, in which the coefficients depend in a non-linear way not only on the state process $X_t$ and its control $u_t$ but also on the…

We introduce a multi-species chemotaxis type system admitting an arbitrarily large number of population species, all of which are attracted vs. repelled by a single chemical substance. The production vs. destruction rates of the chemotactic…

Coarse-graining techniques play a central role in reducing the complexity of stochastic models, and are typically characterised by a mapping which projects the full state of the system onto a smaller set of variables which captures the…

We present and discuss a general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems, able to overcome the intrinsic limitations of the conventional Markov approximation. In particular, the…

This paper introduces a Lyapunov-based control approach with homodyne measurement. We study two filtering approaches: (i) the traditional quantum filtering and (ii) a modified version of the extended Kalman filtering. We examine both…

In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…

We investigate the quantum-classical correspondence in open quantum many-body systems using the SU(3) Bose-Hubbard trimer as a minimal model. Combining exact diagonalization with semiclassical Langevin dynamics, we establish a direct…

We establish the global well-posedness of overdamped dynamic density functional theory (DDFT): a nonlinear, nonlocal integro-partial differential equation used in statistical mechanical models of colloidal fluids, and other applications…

We consider non-conservative positive semigroups and obtain necessary and sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Perron eigenelements and provides…

This paper presents an elementary proof of stochastic stability of a discrete-time reversible Markov chain starting from a Foster-Lyapunov drift condition. Besides its relative simplicity, there are two salient features of the proof: (i) it…

In this work we investigate the long-time behavior, that is the existence and characterization of invariant measures as well as convergence of transition probabilities, for Markov processes obtained as the unique mild solution to stochastic…

For a qualitative analysis of spectra of certain two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful. These methods (and, in particular, a generalization of the concept…

This paper develops sharp Hautus-type criteria, stochastic counterparts of the classical Popov-Belevitch-Hautus test, for exact controllability and stabilizability of backwardstructured stochastic linear systems. The main finding is that…

As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…

In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…

This paper develops a new approach to small time local attainability of smooth manifolds of any dimension, possibly with boundary and to prove H\"older continuity of the minimum time function. We give explicit pointwise conditions of any…

The theory of quantum jump trajectories provides a new framework for understanding dynamical phase transitions in open systems. A candidate for such transitions is the atom maser, which for certain parameters exhibits strong intermittency…

We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…

This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…