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Related papers: Conditional ergodicity in infinite dimension

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In this study, a new extension of the Markov Renewal theory is introduced by allowing time to evolve in multiple dimensions. The resulting chains are referred to as multi-time Markov Renewal chains and since this extension is new, the state…

Probability · Mathematics 2025-08-21 Leonidas Kordalis , Samis Trevezas

We consider Markov chains that obey the following general non-linear state space model: $\Phi_{k+1} = F(\Phi_k, \alpha(\Phi_k, U_{k+1}))$ where the function $F$ is $C^1$ while $\alpha$ is typically discontinuous and $\{U_k: k \in…

Probability · Mathematics 2019-02-07 Alexandre Chotard , Anne Auger

The dissertation describes ergodic properties of some stochastic dynamical systems generated by Markov chains with values in the state space which is a Polish space. The mathematical model describing the process of cell division is…

Probability · Mathematics 2016-03-24 Hanna Wojewódka

Max-stable processes are central models for spatial extremes. In this paper, we focus on some space-time max-stable models introduced in Embrechts et al. (2016). The processes considered induce discrete-time Markov chains taking values in…

Probability · Mathematics 2018-05-09 Erwan Koch , Christian Y. Robert

We study properties of the Laplace transforms of non-negative additive functionals of Markov chains. We are namely interested in a multiplicative ergodicity property used in [18] to study bifurcating processes with ancestral dependence. We…

Probability · Mathematics 2015-09-11 Loïc Hervé , Françoise Pène

In this short note we prove ``effective" geometric ergodicity (i.e a Perron-Frobenius theorem) for Markov chains in random mixing dynamical environment satisfying a random non-uniform version of the Doeblin condition. Effectivity here means…

Probability · Mathematics 2026-01-05 Yeor Hafouta

In this paper we find nonasymptotic exponential upper bounds for the deviation in the ergodic theorem for families of homogeneous Markov processes. We find some sufficient conditions for geometric ergodicity uniformly over a parametric…

Probability · Mathematics 2012-05-10 Leonid Galtchouk , Serguei Pergamenchtchikov

We continue the analysis of nontrivial examples of quantum Markov processes. This is done by applying the construction of entangled Markov chains obtained from classical Markov chains with infinite state--space. The formula giving the joint…

Operator Algebras · Mathematics 2007-05-23 Francesco Fidaleo

In this paper, we study the ergodicity of invariant sublinear expectation of sublinear Markovian semigroup. For this, we first develop an ergodic theory of an expectation-preserving map on a sublinear expectation space. Ergodicity is…

Probability · Mathematics 2021-12-01 Chunrong Feng , Huaizhong Zhao

We discuss the ergodic properties of quasi-Markovian stochastic differential equations, providing general conditions that ensure existence and uniqueness of a smooth invariant distribution and exponential convergence of the evolution…

Probability · Mathematics 2018-11-13 Benedict Leimkuhler , Matthias Sachs

The explicit criteria for several types of ergodicity of one-dimensional diffusions or birth-death processes have been found out recently in a surprisingly short period. One of the criteria is for exponential ergodicity of birth-death…

Probability · Mathematics 2007-05-23 Mu-Fa chen

We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential…

Probability · Mathematics 2015-04-15 Christophe Andrieu , Anthony Lee , Matti Vihola

We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to…

Probability · Mathematics 2023-09-06 Pei-Sen Li , Zenghu Li , Jian Wang , Xiaowen Zhou

The paper provides a systematic characterization of quantum ergodic and mixing channels in finite dimensions and a discussion of their structural properties. In particular, we discuss ergodicity in the general case where the fixed point of…

This paper introduces ergodic-risk criteria, which capture long-term cumulative risks associated with controlled Markov chains through probabilistic limit theorems--in contrast to existing methods that require assumptions of either finite…

Optimization and Control · Mathematics 2025-12-03 Shahriar Talebi , Na Li

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…

Dynamical Systems · Mathematics 2015-05-14 Azam Ehsani , Fatome-Helen Ghane , Marzie Zaj

For a Markov chain $Y$ with values in a Polish space, consider the entrance chain, obtained by sampling $Y$ at the moments when it enters a fixed set $A$ from its complement $A^c$. Similarly, consider the exit chain, obtained by sampling…

Probability · Mathematics 2025-05-15 Aleksandar Mijatovic , Vladislav Vysotsky

We consider periodic Markov chains with absorption. Applying to iterates of this periodic Markov chain criteria for the exponential convergence of conditional distributions of aperiodic absorbed Markov chains, we obtain exponential…

Probability · Mathematics 2022-11-08 Nicolas Champagnat , Denis Villemonais

For a Markov chain $Y$ with values in a Polish space, consider the entrance Markov chain obtained by sampling $Y$ at the moments when it enters a fixed set $A$ from its complement $A^c$. Similarly, consider the exit Markov chain, obtained…

Probability · Mathematics 2020-05-25 Aleksandar Mijatović , Vladislav Vysotsky

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…

Analysis of PDEs · Mathematics 2023-11-01 Elie Abdo , Ruimeng Hu , Quyuan Lin