Related papers: Statistical convergence of Markov experiments to d…
In this paper we present a novel method for estimating the parameters of a parametric diffusion processes. Our approach is based on a closed-form Maximum Likelihood estimator for an approximating Continuous Time Markov Chain (CTMC) of the…
We present a Markov approximation for jump-diffusions whose jump part consists in a Hawkes process with intensity driven by a general (possibly non-monotone) kernel. Under minimal integrability conditions, the kernel can be approximated by…
We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wasserstein distance. These are particularly suited to establishing the cut-off phenomenon for suitable chains.…
We prove the global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a time inhomogeneous jump-diffusion process and a Gaussian white noise experiment. Here,…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
We build and study a recursive algorithm based on the occupation measure of an Euler scheme with decreasing step for the numerical approximation of the quasistationary distribution (QSD) of an elliptic diffusion in a bounded domain. We…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…
In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional…
This article is concerned with sampling from Gibbs distributions $\pi(x)\propto e^{-U(x)}$ using Markov chain Monte Carlo methods. In particular, we investigate Langevin dynamics in the continuous- and the discrete-time setting for such…
We consider a diffusion given by a small noise perturbation of a dynamical system driven by a potential function with a finite number of local minima. The classical results of Freidlin and Wentzell show that the time this diffusion spends…
We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions $\mu^\ast$ in $\mathbb{R}^d$ with a Lebesgue density of the form $\mu^\ast(x) \propto \exp(-f(Kx)-g(x))$, where $K$ is a linear…
This paper considers the level-increment (LI) truncation approximation of M/G/1-type Markov chains. The LI truncation approximation is useful for implementing the M/G/1 paradigm, which is the framework for computing the stationary…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
We study the difference between the probability density of a random variable $F$ on Markov diffusion chaos and the probability density of a general target distribution $Z$. In the special case where $F$ is a chaotic random variables and $Z$…
We introduce a nonparametric model for inferring time-evolving, unobserved probability distributions from discrete-time data consisting of unlabelled partitions. The latent process is a two-parameter Poisson-Dirichlet diffusion, and…
In this paper we study the strong convergence for the Euler-Maruyama approximation of a class of stochastic differential equations whose both drift and diffusion coefficients are possibly discontinuous.
Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…
A model for diffusion in liquids that couples the dynamics of tracer particles to a fluctuating Stokes equation for the fluid is investigated in the limit of large Schmidt number. In this limit, the concentration of tracers is shown to…
The task of sampling from a high-dimensional distribution $\pi$ on $\R^d$ is a fundamental algorithmic problem with applications throughout statistics, engineering, and the sciences. Consider the Langevin diffusion on $\R^d$ \begin{align*}…