Related papers: On ergodicity of some Markov processes
We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are…
We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form \[ {T_f}:{[0, 1) \times \mathbb{R}}\to{[0, 1) \times \mathbb{R}},\quad {T_f(x, t)}:={(T(x),…
Let $\alpha: G\curvearrowright X$ be a minimal free continuous action of an infinite countable amenable group on an infinite compact metrizable space. In this paper, under the hypothesis that the invariant ergodic probability Borel measure…
We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the…
We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with…
A stable-like Markov chain is a time-homogeneous Markov chain on the real line with the transition kernel $p(x,dy)=f_x(y-x)dy$, where the density functions $f_x(y)$, for large $|y|$, have a power-law decay with exponent $\alpha(x)+1$, where…
We consider a control problem for a heterogeneous population composed of agents able to switch at any time between different options. The controller aims to maximize an average gain per time unit, supposing that the population is of…
We study the semiclassical time evolution of observables given by matrix valued pseudodifferential operators and construct a decomposition of the Hilbert space $L^2(\rz^d)\otimes\kz^n$ into a finite number of almost invariant subspaces. For…
In this work, we study ergodicity of continuous time Markov processes on state space $\mathbb{R}_{\geq 0} := [0,\infty)$ obtained as unique strong solutions to stochastic equations with jumps. Our first main result establishes exponential…
The theory of ergodic optimization for distance-expanding maps is extended to Gauss's continued fraction map. Since the set of invariant probability measures is not weak$^*$ closed, we establish a characterisation of the closure of this…
Quantum trajectories are Markov processes that describe the time-evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they are defined as solutions of the so-called "Stochastic Schr\"odinger Equations",…
It is well-known that a strict analogue of the Birkhoff Ergodic Theorem in infinite ergodic theory is trivial; it states that for any infinite-measure-preserving ergodic system the Birkhoff average of every integrable function is almost…
In this review-type paper written at the occasion of the Oberwolfach workshop {\em One-sided vs. Two-sided stochastic processes} (february 22-29, 2020), we discuss and compare Markov properties and generalisations thereof in more…
We consider an electrodiffusion model that describes the intricate interplay of multiple ionic species with a two-dimensional, incompressible, viscous fluid subjected to stochastic additive noise. This system involves nonlocal nonlinear…
In this paper, we propose a novel kind of numerical approximations to inherit the ergodicity of stochastic Maxwell equations. The key to proving the ergodicity lies in the uniform regularity estimates of the numerical solutions with respect…
In this work, we address ergodicity of smooth actions of finitely generated semi-groups on an m-dimensional closed manifold M. We provide sufficient conditions for such an action to be ergodic with respect to the Lebesgue measure. Our…
We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…
This paper is concerned with an extended Galton-Watson process so as to allow individuals to live and reproduce for more than one unit time. We assume that each individual can live $k$ seasons (time-units) with probability $h_k$, and…
A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian…
Consider a uniformly sampled random $d$-regular graph on $n$ vertices. If $d$ is fixed and $n$ goes to $\infty$ then we can relate typical (large probability) properties of such random graph to a family of invariant random processes (called…