Related papers: A large deviation perspective on ratio observables…
We consider a multiscale system of stochastic differential equations in which the slow component is perturbed by a small fractional Brownian motion with Hurst index $H>1/2$ and the fast component is driven by an independent Brownian motion.…
We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…
We establish a large deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, the large deviation principle is derived for super-Brownian…
Quantifying how distinguishable two stochastic processes are lies at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We study large deviations for the current of one-dimensional stochastic particle systems with periodic boundary conditions. Following a recent approach based on an earlier result by Jensen and Varadhan, we compare several candidates for…
In this paper, the large deviations on trajectory level for ergodic Markov processes are studied. These processes take values in the non-negative quadrant of the two dimension lattice and are concentrated on step-wise functions. The rates…
We present dynamic measurements of a lattice gas during phase separation, which we use as an analogy for self-assembly of equilibrium ordered structures. We use two approaches to quantify the degree of 'reversibility' of this process:…
Time evolution in several classes of quantum devices is generated through the application of quantum gates. Resetting is a critical technological feature in these systems allowing for mid-circuit measurement and complete or partial qubit…
We establish a sharp large deviation principle for renewal-reward processes, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. In fact, we demonstrate a weak large deviation principle…
This study focuses on large deviation principles for fully coupled multiscale multivalued stochastic systems, in which the slow component is governed by a multivalued stochastic differential equation and the fast component is described by a…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
In this paper we discuss the dynamics and transport properties of a massive particle, in a time dependent periodic potential of the ratchet type, with a dissipative environment. The directional currents and characteristics of the motion are…
Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate…
In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works…