Related papers: Lorden's inequality and coupling method for backwa…
We give strong bounds for the rate of convergence of the regenerative process distribution to the stationary distribution in the total variation metric. These bounds are obtained by using coupling method. We propose this method for…
The ability to estimate the rate of convergence for the distributions of regenerative processes is in great demand. These processes are often encountered in queuing theory and in related problems. In some papers on regenerative processes,…
In queueing theory, Lorden's inequality can be used for bounds estimation of the moments of backward and forward renewal times. Two random variables called backwards renewal time and forward renewal time for this process are defined.…
We propose a new modification of the coupling method for renewal process in continuous time. We call this modification "the stationary coupling method", and construct it primarily to obtain the bounds for convergence rate of the…
It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only…
We consider renewal-type processes whose positive inter-renewal times may be dependent, non-identically distributed, and may have mixed distributions. We introduce a generalised intensity measure extending the classical hazard-rate…
Via a coupling argument, it is proved that the solution to a renewal equation has a power law decay rate in the case of a spread out interarrival distribution. By the regenerative property, the convergence in distribution for the recurrence…
We use coupling to study the time taken until the distribution of a statistic on a Markov chain is close to its stationary distribution. Coupling is a common technique used to obtain upper bounds on mixing times of Markov chains, and we…
We establish explicit exponential convergence estimates for the renewal theorem, in terms of a uniform component of the inter arrival distribution, of its Laplace transform which is assumed finite on a positive interval, and of the Laplace…
Generalization of the Lorden's inequality is an excellent tool for obtaining strong upper bounds for the convergence rate for various complicated stochastic models. This paper demonstrates a method for obtaining such bounds for some…
Obtaining estimates of the convergence rate of the regenerating process $Q(t)$ whose value at time $t$ is equal to the number of claims in the system $ M \backslash G \backslash \infty $ at this moment, to the limit (stationary) regime.
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
We discuss the concepts of quasi-renewal and quasi-regenerative processes. We also propose a method for obtaining the upper bounds for the convergence rate of the distribution of a regenerative and quasi-regenerative process to a stationary…
A class of random recursive sequences (Y_n) with slowly varying variances as arising for parameters of random trees or recursive algorithms leads after normalizations to degenerate limit equations of the form X\stackrel{L}{=}X. For…
One-shot coupling is a method of bounding the convergence rate between two copies of a Markov chain in total variation distance, which was first introduced by Roberts and Rosenthal and generalized by Madras and Sezer. The method is divided…
A coupling method is developed for univariate extreme value theory , providing an alternative to the use of the tail empirical/quantile processes. Emphasizing the Peak-over-Threshold approach that approximates the distribution above high…
Using coupling techniques based on Stein's method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Taking advantage of modern coupling techniques allows us to…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…