Related papers: Iterated invariance principle for slowly mixing dy…
We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…
We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we explicitly show that dynamical…
Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give…
A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the…
Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
In this paper, we give rates of convergence in the strong invariance principle for non-adapted sequences satisfying projective criteria. The results apply to the iterates of ergodic automorphisms T of the d-dimensional torus, even in the…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
In order to study the invariant measures of discrete KdV- and Toda-type systems, this article focusses on models, discretely indexed in space and time, whose dynamics are deterministic and defined locally via lattice equations. A detailed…
In this paper, we develop a variational foundation for stochastic thermodynamics of finite-dimensional, continuous-time systems. Requiring the second law (non-negative average total entropy production) systematically yields a consistent…
This work focuses on a slow-fast system perturbed by mixed fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. The integral with respect to fractional Brownian motion is the generalized Riemann-Stieltjes integral and the integral…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea…
This paper extends split variational inclusion problems to dynamic, stochastic, and multi-agent systems in Banach spaces. We propose novel iterative algorithms to handle stochastic noise, time-varying operators, and coupled variational…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
A strong invariance principle is established for random fields which satisfy dependence conditions more general than positive or negative association. We use the approach of Cs\"{o}rg\H{o} and R\'{e}v\'{e}sz applied recently by Balan to…
Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical…
This paper has a flaw in an argument that uses the weak-* convergence of measures. The paper was replaced by "Entropy and Its Variational Principle for Locally Compact Metrizable Systems", by the same authors.
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…
This article is concerned with a new filtered two-step variational integrator for solving the charged-particle dynamics in a mildly non-uniform moderate or strong magnetic field with a dimensionless parameter $\varepsilon$ inversely…
In this paper, we give a formulation of the variational iteration method that makes it suitable for the analysis of the solutions of Klein-Gordon equations with variable coefficients. We particularly study a Klein-Gordon problem which has…