Related papers: Evolution of Measures in Nonsmooth Dynamical Syste…

This paper focuses on the performance and the robustness analysis of stochastic jump linear systems. The state trajectory under stochastic jump process becomes random variables, which brings forth the probability distributions in the system…

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…

A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…

The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…

This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…

Quantum measurement is physically realized through a finite dynamical interaction between a system and a measuring apparatus, giving rise to a continuous transition from weak to strong regimes. While this crossover is well understood under…

During a continuous measurement, quantum systems can be described by a stochastic Schr\"odinger equation which, in the appropriate limit, reproduces the von Neumann wave-function collapse. The average behavior on the ensemble of all…

Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

Hybrid evolution protocols, composed of unitary dynamics and repeated, weak or projective measurements, give rise to new, intriguing quantum phenomena, including entanglement phase transitions and unconventional conformal invariance.…

We consider probabilistic models for sequential observations which exhibit gradual transitions among a finite number of states. We are particularly motivated by applications such as human activity analysis where observed accelerometer time…

This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…

Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…

We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…

The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a…

We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…

The stochastic dynamics of small elastic objects in fluid are central to many important and emerging technologies. It is now possible to measure and use the higher modes of motion of elastic structures when driven by Brownian motion alone.…

In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…

This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…