Related papers: On Strong Embeddings by Stein's Method
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…
Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…
Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…
A Schr\"odinger bridge is the most probable time-dependent probability distribution that connects an initial probability distribution $w_{i}$ to a final one $w_{f}$. The problem has been solved and widely used for the case of simple…
In this paper, we investigate the embeddings for topological flows. We prove an embedding theorem for discrete topological system. Our results apply to suspension flows via constant function, and for this case we show an embedding theorem…
Strong approximations of uniform transport processes to the standard Brownian motion rely on the Skorokhod embedding of random walk with centered double exponential increments. In this note we make such an embedding explicit by means of a…
We consider random multiplicative functions taking the values $\pm 1$. Using Stein's method for normal approximation, we prove a central limit theorem for the sum of such multiplicative functions in appropriate short intervals.
This paper develops a new technique for the path approximation of one-dimensional stochastic processes, more precisely the Brownian motion and families of stochastic differential equations sharply linked to the Brownian motion (usually…
In this paper we establish strong embedding theorems, in the sense of the Komlos-Major-Tusnady framework, for the performance metrics of a general class of transitory queueing models of nonstationary queueing systems. The nonstationary and…
String theory predicts that the couplings of Nature descend from dynamical fields. All known string-motivated particle physics models also come with a wide range of possible extra sectors. It is common to posit that such moduli are frozen…
This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random…
We extend the ideas of (Barbour 1990) and use Stein's method to obtain a bound on the distance between a scaled time-changed random walk and a time-changed Brownian Motion. We then apply this result to bound the distance between a…
This article is devoted to methods of construction and study of stochastic models based on Monte Carlo method. A model of Brownian motion, the construction and processing which brings to a world of random numbers and mathematical…
Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…
The rate of strong convergence is investigated for an approximation scheme for a class of stochastic differential equations driven by a time-changed Brownian motion, where the random time changes $(E_t)_{t\ge 0}$ considered include the…
In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…
Let $\{X_{i}, i\in J\}$ be a family of locally dependent non-negative integer-valued random variables with finite expectations and variances. We consider the sum $W=\sum_{i\in J}X_i$ and use Stein's method to establish general upper error…
We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph's spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we…
We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions,…
In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partition. We provide applications in the context of problems that…