Related papers: Stein's method and duality of Markov processes
We study properties of the (generalized) Dickman distribution with two parameters and the stationary solution of the Ornstein-Uhlenbeck stochastic differential equation driven by a Poisson process. In particular, we show that the marginal…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the…
We adapt Stein's method of diffusion approximations, developed by Barbour, to the study of chaotic dynamical systems. We establish an error bound in the functional central limit theorem with respect to an integral probability metric of…
A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…
In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose…
We consider a Markovian jumping process which is defined in terms of the jump-size distribution and the waiting-time distribution with a position-dependent frequency, in the diffusion limit. We assume the power-law form for the frequency.…
In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time.…
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…
The purpose of this dissertation is to introduce a version of Stein's method of exchangeable pairs to solve problems in measure concentration. We specifically target systems of dependent random variables, since that is where the power of…
In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is…
A continuous time mixed state branching process is constructed as the scaling limits of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic…
We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein…
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…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
New bounds for the $k$-th order derivatives of the solutions of the normal and multivariate normal Stein equations are obtained. Our general order bounds involve fewer derivatives of the test function than those in the existing literature.…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
This work focuses on stability analysis of numerical solutions to jump diffusions and jump diffusions with Markovian switching. Due to the use of Poisson processes, using asymptotic expansions as in the usual approach of treating diffusion…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
Convergence rate to the stationary distribution for continuous-time Markov processes can be studied using Lyapunov functions. Recent work by the author provided explicit rates of convergence in special case of a reflected jump-diffusion on…