Related papers: Stochastic Lagrangians for Statistical Dynamics
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be…
A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…
We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum…
We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and…
In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints.We investigate the…
This paper introduces a mathematical framework of a stochastic process model as a generalization of diffusion stochastic processes to model latent variables in categorical responses given unobserved random effects and maximum likelihood…
Stochastic dynamics on sparse graphs and disordered systems often lead to complex behaviors characterized by heterogeneity in time and spatial scales, slow relaxation, localization, and aging phenomena. The mathematical tools and…
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…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
Stochastic systems have a control-theoretic interpretation in which noise plays the role of control. In the weak-noise limit, relevant at low temperatures or in large populations, this leads to a precise mathematical mapping: the most…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…
Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have…
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and the parametric derivatives of statistical quantities are…