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In this paper we introduce a model which provides a new approach to the phenomenon of stochastic resonance. It is based on the study of the properties of the stationary distribution of the underlying stochastic process. We derive the…

Probability · Mathematics 2007-05-23 Peter Imkeller , Ilya Pavlyukevich

The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is…

Probability · Mathematics 2007-06-13 Johan Segers

This paper considers the subexponential asymptotics of the stationary distributions of GI/G/1-type Markov chains in two cases: (i) the phase transition matrix in non-boundary levels is stochastic; and (ii) it is strictly substochastic. For…

Probability · Mathematics 2016-06-22 Tatsuaki Kimura , Hiroyuki Masuyama , Yutaka Takahashi

We show that the convergence of finite state space Markov chains to stationarity can often be considerably speeded up by alternating every step of the chain with a deterministic move. Under fairly general conditions, we show that not only…

Probability · Mathematics 2020-08-27 Sourav Chatterjee , Persi Diaconis

In this paper, we establish novel concentration inequalities for additive functionals of geometrically ergodic Markov chains similar to Rosenthal inequalities for sums of independent random variables. We pay special attention to the…

Probability · Mathematics 2025-09-26 Alain Durmus , Eric Moulines , Alexey Naumov , Sergey Samsonov , Marina Sheshukova

A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We…

Probability · Mathematics 2020-01-10 Yana Belopolskaya , Guodong Pang , Andrey Sarantsev , Yurii Suhov

A sequence of Markov chains is said to exhibit (total variation) cutoff if the convergence to stationarity in total variation distance is abrupt. We consider reversible lazy chains. We prove a necessary and sufficient condition for the…

Probability · Mathematics 2018-01-19 Riddhipratim Basu , Jonathan Hermon , Yuval Peres

The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…

Quantum Physics · Physics 2015-02-20 Vedran Dunjko , Hans J. Briegel

An important step in the Markov reward approach to error bounds on stationary performance measures of Markov chains is to bound the bias terms. Affine functions have been successfully used for these bounds for various models, but there are…

Probability · Mathematics 2019-01-04 Xinwei Bai , Jasper Goseling

We study the convergence rate to stationarity for a class of exchangeable partition-valued Markov chains called cut-and-paste chains. The law governing the transitions of a cut-and-paste chain are determined by products of i.i.d. stochastic…

Probability · Mathematics 2012-09-25 Harry Crane , Steven P. Lalley

In this paper, we give estimates of the quadratic transportation cost in the conditional central limit theorem for a large class of dependent sequences. Applications to irreducible Markov chains, dynamical systems generated by intermittent…

Probability · Mathematics 2022-12-09 Jérôme Dedecker , Florence Merlevède , Emmanuel Rio

We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten…

Mathematical Finance · Quantitative Finance 2016-03-30 Jean-David Fermanian , Hassan Malongo

We obtain variance inequalities for quadratic forms of weakly dependent random variables with bounded fourth moments. We also discuss two application. Namely, we use these inequalities for deriving the limiting spectral distribution of a…

Probability · Mathematics 2016-03-07 Pavel Yaskov

One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional variances are constant. We here show that this property is also…

Statistics Theory · Mathematics 2018-09-24 Lukas Steinberger , Hannes Leeb

We study stochastic extinction for a class of Markov processes motivated by models in ecology and epidemiology. Extinction is often characterized by a boundedness condition and a condition on boundary Lyapunov exponents (invasion rates).…

Probability · Mathematics 2026-04-23 Nhu Nguyen , Dang H. Nguyen

Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…

Methodology · Statistics 2024-03-12 William K. Schwartz , Sonja Petrović , Hemanshu Kaul

Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form.…

Probability · Mathematics 2021-12-07 Beatriz Pascual-Escudero , Linard Hoessly

In this paper we consider stationary Markov chains with trivial two-sided tail sigma field, and prove that additive functionals satisfy the central limit theorem provided the variance of partial sums divided by n is bounded.

Probability · Mathematics 2022-09-01 Magda Peligrad

The existence of stationary distributions to distribution dependent stochastic differential equations are investigated by using the ergodicity of the associated decoupled equation and the Schauder fixed point theorem. By using Zvonkin's…

Probability · Mathematics 2021-05-14 Shao-Qin Zhang

For a stochastically monotone Markov chain taking values in a Polish space, we present a number of conditions for existence and for uniqueness of its stationary regime, as well as for closeness of its transient trajectories. In particular,…

Probability · Mathematics 2026-04-02 Sergey Foss , Michael Scheutzow