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We develop a functional Stein-Malliavin method in a non-diffusive Poissonian setting, thus obtaining a) quantitative central limit theorems for approximation of arbitrary non-degenerate Gaussian random elements taking values in a separable…
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…
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…
Consider the standard stochastic reaction network model where the dynamics is given by a continuous-time Markov chain over a discrete lattice. For such models, estimation of parameter sensitivities is an important problem, but the existing…
We show how the infinitesimal exchangeable pairs approach to Stein's method combines naturally with the theory of Markov semigroups. We present a multivariate normal approximation theorem for functions of a random variable invariant with…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
Let W be either the number of descents or inversions of a permutation. Stein's method is applied to show that W satisfies a central limit theorem with error rate n^(-1/2). The construction of an exchangeable pair (W,W') used in Stein's…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
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…
The concentration inequality approach for normal approximation by Stein's method is generalized to the multivariate setting. We use this approach to prove a non-smooth function distance for multivariate normal approximation for standardized…
We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and…
We prove a Poisson limit theorem in the total variation distance of functionals of a general Poisson point process using the Malliavin-Stein method. Our estimates only involve first and second order difference operators and are closely…
Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and…
Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…
This article derives quantitative limit theorems for multivariate Poisson and Poisson process approximations. Employing the solution of Stein's equation for Poisson random variables, we obtain an explicit bound for the multivariate Poisson…
This paper establishes quantitative limit theorems for two classes of Cox point processes, quantifying their convergence to a Poisson point process (PPP). We employ Stein's method for PPP aproximation, leveraging the generator approach and…
In this paper, we revisit the original ideas of Stein and propose an estimator of the intensity parameter of a homogeneous Poisson point process defined in $\R^d$ and observed in a bounded window. The procedure is based on a new general…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
Stein's method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation the functional equation is a first order differential equation. Malliavin calculus is an…
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…