Related papers: Approximate moment dynamics for polynomial and tri…
Many stochastic continuous-state dynamical systems can be modeled as probabilistic programs with nonlinear non-polynomial updates in non-nested loops. We present two methods, one approximate and one exact, to automatically compute, without…
This paper proposes a semidefinite programming based method for estimating moments of a stochastic hybrid system (SHS). For polynomial SHSs -- which consist of polynomial continuous vector fields, reset maps, and transition intensities --…
In this paper, we address the problem of uncertainty propagation through nonlinear stochastic dynamical systems. More precisely, given a discrete-time continuous-state probabilistic nonlinear dynamical system, we aim at finding the sequence…
Compartmentalised biochemical reactions are a ubiquitous building block of biological systems. The interplay between chemical and compartmental dynamics can drive rich and complex dynamical behaviors that are difficult to analyse…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
We propose a method to compute an approximation of the moments of a discrete-time stochastic polynomial system. We use the Carleman linearization technique to transform this finite-dimensional polynomial system into an infinite-dimensional…
We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states…
We develop a moment equation closure minimization method for the inexpensive approximation of the steady state statistical structure of nonlinear systems whose potential functions have bimodal shapes and which are subjected to correlated…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
Stochastic Hybrid Systems (SHS) constitute an important class of mathematical models that integrate discrete stochastic events with continuous dynamics. The time evolution of statistical moments is generally not closed for SHS, in the sense…
In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
The derivation of dynamical laws for general observables (or moments) from the master equation for the probability distribution remains a challenging problem in statistical physics. Here, we present an alternative formulation of the general…
In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier…
Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…
Moment systems arise in a wide range of contexts and applications, e.g. in network modeling of complex systems. Since moment systems consist of a high or even infinite number of coupled equations, an indispensable step in obtaining a…
Given a stochastic dynamical system modelled via stochastic differential equations (SDEs), we evaluate the safety of the system through characterizations of its exit time moments. We lift the (possibly nonlinear) dynamics into the space of…
In the present work, an approach to the moment closure problem on the basis of orthogonal polynomials derived from Gram matrices is proposed. Its properties are studied in the context of the moment closure problem arising in gas kinetic…
This paper studies a novel approach for approximating the behavior of compartmental spreading processes. In contrast to prior work, the methods developed describe a dynamics which bound the exact moment dynamics, without explicitly…
Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…
We present a general numerical scheme for the practical implementation of statistical moment closures suitable for modeling complex, large-scale, nonlinear systems. Building on recently developed equation-free methods, this approach…