Related papers: Distance Between Stochastic Linear Systems

Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial…

We identify the leading term in the asymptotics of the quadratic Wasserstein distance between the invariant measure and empirical measures for diffusion processes on closed weighted four-dimensional Riemannian manifolds. Unlike results in…

To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…

We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic…

Most Kalman filters for non-linear systems, such as the unscented Kalman filter, are based on Gaussian approximations. We use Poincar\'e inequalities to bound the Wasserstein distance between the true joint distribution of the prediction…

Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $\alpha$-stable L\'evy process is still lacking.…

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite…

This paper is motivated by the problem of quantitatively bounding the convergence of adaptive control methods for stochastic systems to a stationary distribution. Such bounds are useful for analyzing statistics of trajectories and…

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…

Detecting relevant changes in dynamic time series data in a timely manner is crucially important for many data analysis tasks in real-world settings. Change point detection methods have the ability to discover changes in an unsupervised…

Ensemble systems appear frequently in many engineering applications and, as a result, they have become an important research topic in control theory. These systems are best characterized by the evolution of their underlying state…

To deal with stochastic hybrid systems with general state-dependent switching, we propose an approximation method by a sequence of stochastic hybrid systems with piecewise constant type switching. The convergence rate in the Wasserstein…

We derive a relation between the dissipation in a stochastic dynamics and the Wasserstein distance. We show that the minimal amount of dissipation required to transform an initial state to a final state during a diffusion process is given…

Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…

We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure…

Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…

The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…

Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…

This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with…

A system's internal dynamics and its interaction with the environment can be determined by tracking how external perturbations affect its transition rates between states. Quantitative measurements of these rates are crucial for optimizing…