Related papers: Long Term Effects of Small Random Perturbations on…

Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental…

An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps,…

The modeling of turbulence, whether it be numerical or analytical, is a difficult challenge. Turbulence is amenable to analysis with linear theory if it is subject to rapid distortions, i.e., motions occurring on a time scale that is short…

Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…

This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…

We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.

In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged…

An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a…

This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…

We study the fluctuations of systems modeled by Markov jump processes with periodic generators. We focus on observables defined through time-periodic functions of the system's states or transitions. Using large deviation theory, canonical…

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…

We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…

Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…

In this article, we prove that a small random perturbation of dynamical system with multiple stable equilibria converges to a Markov chain whose states are neighborhoods of the deepest stable equilibria, under a suitable time-rescaling,…

We consider the long-time behavior of systems close to a system with a smooth first integral. Under certain assumptions, the limiting behavior, to some extent, turns out to be universal: it is determined by the first integral, the…

A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…

Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

The short-time dynamics of correlated systems is strongly influenced by initial correlations giving rise to an additional collision integral in the non-Markovian kinetic equation. Exact cancellation of the two integrals is found if the…