相关论文: Non-convergence to unstable equilibriums for conti…

Non-equilibrium molecular dynamics simulations are used to demonstrate the asymptotic convergence of the Transient and Steady State forms of the Fluctuation Theorem. In the case of planar Poiseuille flow, we find that the Transient form,…

Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…

Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical…

We study the rate of convergence to equilibrium of the self-repellent random walk and its local time process on the discrete circle $\mathbb{Z}_n$. While the self-repellent random walk alone is non-Markovian since the jump rates depend on…

We investigate the convergence of McKean-Vlasov diffusions in a nonconvex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures…

This report considers a variable step time discretization algorithm proposed by Dahlquist, Liniger and Nevanlinna and applies the algorithm to the unsteady Stokes/Darcy model. Although long-time forgotten and little explored, the algorithm…

First, sufficient conditions are given for a triangular array of random vectors such that the sequence of related random step functions converges towards a (not necessarily time homogeneous) diffusion process. These conditions are weaker…

We study the convergence behavior of the stochastic heavy-ball method with a small stepsize. Under a change of time scale, we approximate the discrete method by a stochastic differential equation that models small random perturbations of a…

Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of…

Non-equilibrium steady states for chains of oscillators (masses) connected by harmonic and anharmonic springs and interacting with heat baths at different temperatures have been the subject of several studies. In this paper, we show how…

The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a…

We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…

This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…

We introduce a novel type of random perturbation for the classical Lorenz flow in order to better model phenomena slowly varying in time such as anthropogenic forcing in climatology and prove stochastic stability for the unperturbed flow.…

It is well known that random walks in one dimensional random environment can exhibit subdiffusive behavior due to presence of traps. In this paper we show that the passage times of different traps are asymptotically independent exponential…

We develop non-equilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in non-ergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate…

We show that the total entropy production in stochastic processes with odd-parity variables (under time reversal) is separated into three parts, only two of which satisfy the integral fluctuation theorems in general. One is the usual excess…

Steady state fluctuation relations for dynamical systems are commonly derived under the assumption of some form of time-reversibility and of chaos. There are, however, cases in which they are observed to hold even if the usual notion of…

In this paper we investigate how the bootstrap can be applied to time series regressions when the volatility of the innovations is random and non-stationary. The volatility of many economic and financial time series displays persistent…

Non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels are considered. It is shown that their stability properties can be studied in terms of an associated class of piecewise deterministic Markov processes,…