Related papers: Density convergence on Markov diffusion chaos via …

We investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density of all local times on the range, at any…

We use the Stein-Chen method to prove new explicit inequalities for the total variation, Wasserstein and local distances between the distribution of a random diagonal sum of a Bernoulli matrix and a Poisson distribution. Approximation…

Denoising diffusion models are a recent class of generative models exhibiting state-of-the-art performance in image and audio synthesis. Such models approximate the time-reversal of a forward noising process from a target distribution to a…

We consider the Markov random flight $\bold X(t)$ in the Euclidean space $\Bbb R^m, \; m\ge 2,$ starting from the origin $\bold 0\in\Bbb R^m$ that, at Poisson-paced times, changes its direction at random according to arbitrary distribution…

A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…

By the continuous mapping theorem, if a sequence of $d$-dimensional random vectors $(\mathbf{W}_n)_{n\geq1}$ converges in distribution to a multivariate normal random variable $\Sigma^{1/2}\mathbf{Z}$, then the sequence of random variables…

In this work we tackle the problem of estimating the density $ f_X $ of a random variable $ X $ by successive smoothing, such that the smoothed random variable $ Y $ fulfills the diffusion partial differential equation $ (\partial_t -…

In this paper we study Markov chains associated with the Metropolis-Hastings algorithm. We consider conditions under which the sequence of the successive densities of such a chain converges to the target density according to the total…

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that…

Density-dependent Markov chains form an important class of continuous-time Markov chains in population dynamics. On any fixed time window [0, T ], when the scale parameter K > 0 is large such chains are well approximated by the solution of…

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…

In this paper we apply the Diffusion approximation procedure to a discrete time Adaptive Markov Chain Monte Carlo (AMCMC) method when the target distribution is standard Normal. We show that the limiting distribution of the diffusion admits…

In this paper, we study first the problem of nonparametric estimation of the stationary density $f$ of a discrete-time Markov chain $(X_i)$. We consider a collection of projection estimators on finite dimensional linear spaces. We select an…

We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…

The probability density function (PDF) of the gas density in turbulent supersonic flows is investigated with high-resolution numerical simulations. In a systematic study, we compare the density statistics of compressible turbulence driven…

We study the Wasserstein gradient flow of the Sinkhorn divergence when both the source and the target are Gaussian distributions. We prove the existence of a flow that stays in the class of Gaussian distributions, and is unique in the…

We study the dynamical exponents $d_{w}$ and $d_{s}$ for a particle diffusing in a disordered medium (modeled by a percolation cluster), from the regime of extreme disorder (i.e., when the percolation cluster is a fractal at $p=p_{c}$) to…

We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…

We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool…