Related papers: Stochastic stability of invariant measures: The 2D…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability.…
The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and…
In this work we set the stage for a new probabilistic pathwise approach to effectively calibrate a general class of stochastic nonlinear fluid dynamics models. We focus on a 2D Euler SALT equation, showing that the driving stochastic…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
This is a survey highlighting several recent results concerning well/ill posedness of the Euler system of gas dynamics. Solutions of the system are identified as limits of consistent approximations generated either by physically more…
We establish the conditioned stochastic stability of equilibrium states for H\"older potentials on uniformly hyperbolic sets. While standard stochastic stability characterises measures on attractors, we analyse the statistics of transient…
Dynamical equations describing physical systems at statistical equilibrium are commonly extended by mathematical tools called "thermostats". These tools are designed for sampling ensembles of statistical mechanics. We propose a dynamic…
Dynamical system properties give rise to effects in Statistical Mechanics. Topological index changes can be the basis for phase transitions. The Euler characteristic is a versatile topological invariant that can be evaluated for model…
Given a dynamical system with a uniformly hyperbolic (`chaotic') attractor, the physically relevant Sinai-Ruelle-Bowen (SRB) measure can be obtained as the limit of the dynamical evolution of the leaf volume along local unstable manifolds.…
In this paper we examine the linear stability of equilibrium solutions to incompressible Euler's equation in 2- and 3-dimensions. The space of perturbations is split into two classes - those that preserve the topology of vortex lines and…
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
We establish the existence and uniqueness of an ergodic invariant measure for 2D fractionally dissipated stochastic Euler equations on the periodic box, for any power of the dissipation term.
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
In this article we show that a large class of infinite measure preserving dynamical systems that do not admit physical measures nevertheless exhibit strong statistical properties. In particular, we give sufficient conditions for existence…