相关论文: Approximating the Markov Chain of the Curie-Weiss …
We develop a new technique, based on Stein's method, for comparing two stationary distributions of irreducible Markov Chains whose update rules are `close enough'. We apply this technique to compare Ising models on $d$-regular expander…
We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of…
We study an approximation method of stationary characters of a two-dimensional Markov chain via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the…
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…
We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's…
An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general…
A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to…
Stochastic Chemical Reaction Networks are continuous time Markov chain models that describe the time evolution of the molecular counts of species interacting stochastically via discrete reactions. Such models are ubiquitous in systems and…
This paper uses the generator approach of Stein's method to analyze the gap between steady-state distributions of Markov chains and diffusion processes. Until now, the standard way to invoke Stein's method for this problem was to use the…
One of the key ingredients to successfully apply Stein's method for distributional approximation are solutions to the Stein equations and their derivatives. Using Barbour's generator approach, one can solve for the solutions to the Stein…
We consider two finite population Markov chain models, the two-island Wright-Fisher model with mutation, and the seed-bank model with mutation. Despite the relatively simple descriptions of the two processes, the the exact form of their…
Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…
This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve…
Let $(W,W')$ be an exchangeable pair. Assume that \[E(W-W'|W)=g(W)+r(W),\] where $g(W)$ is a dominated term and $r(W)$ is negligible. Let $G(t)=\int_0^tg(s)\,ds$ and define $p(t)=c_1e^{-c_0G(t)}$, where $c_0$ is a properly chosen constant…
This work presents the first systematic development of Stein's method for matrix distributions. We establish the basic essential ingredients of Stein's method for matrix normal approximation: we derive a generator-based Stein identity from…
In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the solution to the Stein equation, we use tools from stochastic…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
A stochastic ordering approach is applied with Stein's method for approximation by the equilibrium distribution of a birth-death process. The usual stochastic order and the more general s-convex orders are discussed. Attention is focused on…
Diffusion approximations have been a popular tool for performance analysis in queueing theory, with the main reason being tractability and computational efficiency. This dissertation is concerned with establishing theoretical guarantees on…
This paper studies the rate of convergence of a family of continuous-time Markov chains (CTMC) to a mean-field model. When the mean-field model is a finite-dimensional dynamical system with a unique equilibrium point, an analysis based on…