Stein's method and birth-death processes
From MaRDI portal
Publication:1872227
DOI10.1214/aop/1015345606zbMath1019.60019OpenAlexW2063452870MaRDI QIDQ1872227
Publication date: 6 May 2003
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aop/1015345606
Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Probability distributions: general theory (60E05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)
Related Items (46)
Compound Poisson process approximation. ⋮ Approximating the number of successes in independent trials: binomial versus Poisson ⋮ Multivariate Poisson and Poisson process approximations with applications to Bernoulli sums and -statistics ⋮ A Pólya Approximation to the Poisson-Binomial Law ⋮ Compound Poisson approximation ⋮ Stein's Method and Stochastic Orderings ⋮ Stein's method, Palm theory and Poisson process approximation. ⋮ On Stein's factors for Poisson approximation in Wasserstein distance ⋮ Zero biasing and a discrete central limit theorem ⋮ Some characterizations and properties of COM-Poisson random variables ⋮ The Prelimit Generator Comparison Approach of Stein’s Method ⋮ Approximating dependent rare events ⋮ Stein's method and Poisson process approximation for a class of Wasserstein metrics ⋮ On approximation of Markov binomial distributions ⋮ Approximation for counts of 2-runs in a two state Markov chain ⋮ A large sample property in approximating the superposition of i.i.d. finite point processes ⋮ Approximations related to the sums of \(m\)-dependent random variables ⋮ Compound Poisson approximations for sums of 1-dependent random variables. I ⋮ Binomial approximation to locally dependent collateralized debt obligations ⋮ On Stein's method for stochastically monotone single-birth chains ⋮ On Stein's method, smoothing estimates in total variation distance and mixture distributions ⋮ On Negative Binomial Approximation to k-Runs ⋮ Intertwining and commutation relations for birth-death processes ⋮ On the asymptotics of locally dependent point processes ⋮ A generalized false discovery rate in microarray studies ⋮ A new metric between distributions of point processes ⋮ On moderate deviations in Poisson approximation ⋮ Stein's method for discrete Gibbs measures ⋮ A polynomial birth-death point process approximation to the Bernoulli process ⋮ Hitting time and mixing time bounds of Stein's factors ⋮ Removing logarithms in Poisson approximation to the partial sum process of a Markov chain ⋮ Nonuniform Approximations for Sums of Discrete m-Dependent Random Variables ⋮ Smoothing effect of compound Poisson approximations to the distributions of weighted sums ⋮ On local estimates and the Stein method ⋮ Approximation for counts of head runs ⋮ Approximation of the difference of two Poisson-like counts by Skellam ⋮ COM-negative binomial distribution: modeling overdispersion and ultrahigh zero-inflated count data ⋮ Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to \(U\)-statistics and stochastic geometry ⋮ Poisson type approximations for the Markov binomial distribution ⋮ On customer flows in jackson queueing networks ⋮ Fluctuations in a general preferential attachment model via Stein's method ⋮ Polynomial birth-death distribution approximation in the Wasserstein distance ⋮ Power Laws in Preferential Attachment Graphs and Stein's Method for the Negative Binomial Distribution ⋮ On Stein's factors for Poisson approximation in Wasserstein distance with nonlinear transportation costs ⋮ Stein's method for conditional compound Poisson approximation ⋮ Stein factors for negative binomial approximation in Wasserstein distance
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Binomial approximation to the Poisson binomial distribution
- Two moments suffice for Poisson approximations: The Chen-Stein method
- Stein's method and multinomial approximation
- Stein's method and point process approximation
- Compound Poisson approximation for nonnegative random variables via Stein's method
- Poisson approximation for dependent trials
- Markov chain models - rarity and exponentiality
- Poisson approximation and the Chen-Stein method. With comments and a rejoinder by the authors
- Removing logarithms from Poisson process error bounds.
- Negative binomial approximation with Stein's method
- On the rate of Poisson convergence
- A probabilistic proof of Stein's factors
- Poisson perturbations
- Compound Poisson Approximation for Dissociated Random Variables via Stein's Method
- Poisson approximation for some statistics based on exchangeable trials
This page was built for publication: Stein's method and birth-death processes
