相关论文: On the Relationship between Mutual Information and…

The model considered is that of ``signal plus white noise.'' Known connections between the noncausal filtering error and mutual information are combined with new ones involving the causal estimation error, in a general abstract setup. The…

Biological neural systems encode and transmit information as patterns of activity tracing complex trajectories in high-dimensional state-spaces, inspiring alternative paradigms of information processing. Heteroclinic networks, naturally…

This paper studies the rich dynamics of one-dimensional granular media equations with attractive quadratic interactions. Building on the monotone dynamical systems framework developed in an earlier work, we allow for multiplicative noise,…

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

Several types of stochastic equations are important in thermodynamics, chemistry, evolutionary biology, population dynamics and quantitative social science. For systems with pair interactions four different types of equations are derived,…

Stochastic resonance is a phenomenon where the response signal to external driving is enhanced by environment noise. In quantum regime, the effect of environment is often intrinsically non-Markovian. Due to the combination of such…

Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…

Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…

Mutual information is a nonlinear measure used in time series analysis in order to measure the linear and non-linear correlations at any lag $\tau$. The aim of this study is to evaluate some of the most commonly used mutual information…

The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…

Chaotic synchronization is generally extremely sensitive to the presence of noise and other inference in the channel. Is this sensitivity a fundamental property of chaotic synchronization or is it related to the choice of synchronization…

Information flow or information transfer is an important concept in dynamical systems which has applications in a wide variety of scientific disciplines. In this study, we show that a rigorous formalism can be established in the context of…

We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…

We investigate the incremental stability properties of It\^o stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two…

Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity.…

Stochastic methods are ubiquitous to a variety of fields, ranging from Physics to Economy and Mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in…

This paper deals with the problem of identifying and estimating dynamical parameters of continuous-time quantum open systems, in the input-output formalism. First, we characterise the space of identifiable parameters for ergodic dynamics,…

In this paper, we study the problem of how to optimally steer the state covariance of a general continuous-time linear stochastic system over a finite time interval subject to additive noise. Optimality here means reaching a target state…