Journal Article10.1007/BF01197887
Stein's method for diffusion approximations
299
TL;DR: In this article, an appropriate analogue of the one-dimensional Stein equation is derived, and the necessary properties of its solutions are established, applied to the partial sums of stationary sequences and of dissociated arrays, to a process version of the Wald-Wolfowitz theorem and to the empirical distribution function.
read more
Abstract: Stein's method of obtaining distributional approximations is developed in the context of functional approximation by the Wiener process and other Gaussian processes. An appropriate analogue of the one-dimensional Stein equation is derived, and the necessary properties of its solutions are established. The method is applied to the partial sums of stationary sequences and of dissociated arrays, to a process version of the Wald-Wolfowitz theorem and to the empirical distribution function.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
5.9K
•Book
Normal Approximation by Stein's Method
Louis H. Y. Chen,Larry Goldstein,Qi-Man Shao +2 more
- 04 Nov 2010
TL;DR: In this paper, Stein's method is used for non-linear statistics and multivariate normal approximations for independent random variables with moderate deviations, and a non-normal approximation for nonlinear statistics.
Stein's method on Wiener chaos
Ivan Nourdin,Giovanni Peccati +1 more
TL;DR: In this paper, the authors combine Malliavin calculus with Stein's method to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process.
Poisson Approximation and the Chen-Stein ethod
Richard Arratia,Larry Goldstein,Louis Gordon +2 more
- 01 Jan 2013
TL;DR: The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution as mentioned in this paper, in many cases, this bound may be given in terms of first and second moments alone.
277
Stein's method and the zero bias transformation with application to simple random sampling
Larry Goldstein,Gesine Reinert +1 more
TL;DR: The zero bias transformation as mentioned in this paper is a generalization of the size bias transformation for non-negative variables, but is applied to variables taking on both positive and negative values, and can also be defined on more general random objects.
References
•Book
Convergence of Probability Measures
Patrick Billingsley
- 01 Jan 1968
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
15K
•Book
Markov Processes: Characterization and Convergence
Stewart N. Ethier,Thomas G. Kurtz +1 more
- 04 Apr 1986
TL;DR: In this paper, the authors present a flowchart of generator and Markov Processes, and show that the flowchart can be viewed as a branching process of a generator.
6.2K
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
5.9K
•Book
Martingale Limit Theory and Its Application
Peter Hall,E Lukacs,Z W Birnbaum,C. C. Heyde +3 more
- 23 Sep 2014
4K