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We study the rate of convergence of the Markov chain on $S_n$ which starts with a random $(n-k)$-cycle for a fixed $k \geq 1$, followed by random transpositions. The convergence to the stationary distribution turns out to be of order $n$.…

Probability · Mathematics 2018-03-26 Alperen Y. Özdemir

We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a "positive…

Probability · Mathematics 2010-11-11 Aldéric Joulin , Yann Ollivier

This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…

Probability · Mathematics 2018-05-07 Zeyu Zheng , Harsha Honnappa , Peter W. Glynn

In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…

Dynamical Systems · Mathematics 2025-09-22 Bryn Davies , Angelica Yu Xiao

In this paper, we study discrete approximation of reflected Brownian motions on domains in Euclidean space. Our approximation is given by a sequence of Markov chains on partitions of the domain, where we allow uneven or random partitions.…

Probability · Mathematics 2025-04-09 Masanori Hino , Arata Maki , Kouhei Matsuura

The paper is concerned with the approximation of the deterministic the mean field type control system by a mean field Markov chain. It turns out that the dynamics of the distribution in the approximating system is described by a system of…

Optimization and Control · Mathematics 2023-08-07 Yurii Averboukh

A rigorous theory of diffraction scattering from extended objects is proposed. The present theory is based on a multiple asymptotic expansion of an integral equation for the exact wave function in terms of the large parameters of the…

Other Condensed Matter · Physics 2016-06-17 Gennady V. Kovalev

It is proved that the limit of the normalized rate-distortion functions of block independent approximations of an irreducible, aperiodic Markoff chain is independent of the initial distribution of the Markoff chain and thus, is also equal…

Information Theory · Computer Science 2018-03-28 Mukul Agarwal

We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by…

Formal Languages and Automata Theory · Computer Science 2016-06-27 Przemysław Daca , Thomas A. Henzinger , Jan Křetínský , Tatjana Petrov

Markov chain Monte Calro methods (MCMC) are commonly used in Bayesian statistics. In the last twenty years, many results have been established for the calculation of the exact convergence rate of MCMC methods. We introduce another rate of…

Statistics Theory · Mathematics 2014-02-17 Kengo Kamatani

In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…

Mathematical Physics · Physics 2015-05-13 Clement Pellegrini , Francesco Petruccione

In this article, we obtain properties of the law associated to the first hitting time of a threshold by a one-dimensional uniformly elliptic diffusion process and to the associated process stopped at the threshold. Our methodology relies on…

Probability · Mathematics 2016-09-30 Noufel Frikha , Arturo Kohatsu-Higa , Libo Li

Diffusion of symmetric diblock copolymer chains in macroscopically oriented lamellar block copolymers are studied in a molecular dynamics simulation. Results for diffusion constant both parallel $D_\parallel$ and perpendicular $D_\perp$ to…

Soft Condensed Matter · Physics 2008-02-03 Michael Murat , Gary S. Grest , Kurt Kremer

We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on…

Statistical Mechanics · Physics 2026-01-15 Pelerine Tsobgni Nyawo , Hugo Touchette

In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a…

Probability · Mathematics 2010-09-01 Zhen-Qing Chen , Panki Kim , Takashi Kumagai

The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in…

Probability · Mathematics 2009-02-06 Sanda N. Socoll , A. D. Barbour

Consider a non-symmetric generalized diffusion $X(\cdot)$ in ${\bbR}^d$ determined by the differential operator $A(\msx)=-\sum_{ij} \partial_ia_{ij}(\msx)\partial_j +\sum_i b_i(\msx)\partial_i$. In this paper the diffusion process is…

Probability · Mathematics 2010-03-16 Nedzad Limić

The main purpose of this paper is to explore the structure of local and regular Dirichlet forms associated with symmetric linear diffusions. Let $(\mathcal{E},\mathcal{F})$ be a regular and local Dirichlet form on $L^2(I,m)$, where $I$ is…

Probability · Mathematics 2018-04-03 Liping Li , Jiangang Ying

We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and…

We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…

Probability · Mathematics 2023-11-29 Guillaume Kon Kam King , Andrea Pandolfi , Marco Piretto , Matteo Ruggiero