A quantitative Heppes Theorem and multivariate Bernoulli distributions

更正：多元CARMA过程、连续时间状态空间模型及采样过程新息的完全正则性，Bernoulli 18, pp. 46-63, 2012

Correction to: Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes, Bernoulli 18, pp. 46-63, 2012

该论文修正了连续时间状态空间模型与MCARMA过程等价性证明中的缺陷，并解决了相关定理问题，确认任何MCARMA过程及线性状态空间模型均具有控制器和观测器规范表示。

Multivariate Poisson and Poisson process approximations with applications to Bernoulli sums and $U$-statistics

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 approximation of random vectors in the Wasserstein distance. The bound is then utilized in the context of point processes to provide a Poisson process approximation result in terms of a new metric called $d_π$, stronger than the total variation distance, defined as the supremum over all Wasserstein distances between random vectors obtained by evaluating the …

Krawtchouk-Griffiths Systems II: As Bernoulli Systems

We call Krawtchouk-Griffiths systems, KG-systems, systems of multivariate polynomials orthogonal with respect to corresponding multinomial distributions. The original Krawtchouk polynomials are orthogonal with respect to a binomial distribution. Here we present a Fock space construction with raising and lowering operators. The operators of "multiplication by X" are found in terms of boson operators and corresponding recurrence relations presented. The Riccati partial differential equations for the differentiation operators, Berezin transform and associated partial differential equations are fo…

Sarmanov copulas的随机表示

Stochastic representation of Sarmanov copulas

本文提出了一种双变量Sarmanov copulas的随机表示方法，通过伯努利混合构造高维copulas，并推导了Spearman和Kendall的精确界限。

Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences

Berry-Esseen bounds for non-linear functionals of infinite Rademacher sequences are derived by means of the Malliavin-Stein method. Moreover, multivariate extensions for vectors of Rademacher functionals are shown. The results establish a connection to small-ball probabilities and shed new light onto the relation between central limit theorems on the Rademacher chaos and norms of contraction operators. Applications concern infinite weighted 2-runs, a combinatorial central limit theorem and traces of Bernoulli random matrices.

Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions

We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our examples include the Moran model in population genetics and its variants in community ecology, the Dirichlet-multinomial Gibbs sampler, a class of generalized Bernoulli--Laplace processes, a generalized Ehrenfest urn model and the multivariate normal autoregressive process.