Two-sided inequalities for the density function's maximum of weighted sum of chi-square variables

A full proof of universal inequalities for the distribution function of the binomial law

We present a new form and a short full proof of explicit two-sided estimates for the distribution function F_{n,p}(x) of the binomial law from the paper published by D.Alfers and H.Dinges in 1984. These inequalities are universal (valid for all binomial distribution and all values of argument) and exact (namely, the upper bound for F_{n,p}(k) is the lower bound for F_{n,p}(k+1)). By means of such estimates it is possible to bound any quantile of the binomial law by 2 subsequent integers.

上下有序的中国餐厅过程及其双侧移民、退居和扩散极限

Up-down ordered Chinese restaurant processes with two-sided immigration, emigration and diffusion limits

本文研究了上下有序中国餐厅过程的缩放极限，扩展了三参数族模型，揭示了泊松-迪里赫利特分布的参数范围扩展及其在相关过程中的应用。

Concentration functions and entropy bounds for discrete log-concave distributions

Two-sided bounds are explored for concentration functions and Rényi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.

Johnson-Schechtman inequalities for noncommutative martingales

In this paper we study Johnson-Schechtman inequalities for noncommutative martingales. More precisely, disjointification inequalities of noncommutative martingale difference sequences are proved in an arbitrary symmetric operator space $E(\mathcal{M})$ of a finite von Neumann algebra $\mathcal{M}$ without making any assumption on the Boyd indices of $E$. We show that we can obtain Johnson-Schechtman inequalities for arbitrary martingale difference sequences and that, in contrast with the classical case of independent random variables or the noncommutative case of freely independent random vari…

Two-sided bounds for degenerate processes with densities supported in subsets of R^N

We obtain two-sided bounds for the density of stochastic processes satisfying a weak Hörmander condition. In particular we consider the cases when the support of the density is not the whole space and when the density has various asymptotic regimes depending on the starting/final points considered (which are as well related to the number of brackets needed to span the space in Hörmander's theorem). The proofs of our lower bounds are based on Harnack inequalities for positive solutions of PDEs whereas the upper bounds derive from the probabilistic representation of the density given by the Mall…

Turán type inequalities for Tricomi confluent hypergeometric functions

Some sharp two-sided Turán type inequalities for parabolic cylinder functions and Tricomi confluent hypergeometric functions are deduced. The proofs are based on integral representations for quotients of parabolic cylinder functions and Tricomi confluent hypergeometric functions, which arise in the study of the infinite divisibility of the Fisher-Snedecor F distribution. Moroever, some complete monotonicity results are given concerning Turán determinants of Tricomi confluent hypergeometric functions. These complement and improve some of the results of Ismail and Laforgia [23].

球面上和高斯空间中的集中不等式最优常数

Optimal constants in concentration inequalities on the sphere and in the Gauss space

本文研究球面和高斯空间中函数偏离中位数和均值的集中不等式，给出最优常数的界，改进了现有文献中的结果。

Malliavin calculus and decoupling inequalities in Banach spaces

We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banach spaces. In the white noise case we obtain two sided L^p-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-Ito chaoses. Our main tools are decoupling inequalities for vector-valued random variables. In the opposite direction we use Meyer's inequalities to give a new proof of a decoupling result for Gaussian …

$L^1$ 解的存在性与唯一性：关于具有随机单边 Osgood 型生成元的多维 BSDEs

Existence and uniqueness on $L^1$ solutions of multidimensional BSDEs with generators of stochastic one-sided Osgood type

本文针对生成元满足随机单边 Osgood 条件、一般增长条件和随机 Lipschitz 条件的多维 BSDEs，在施加额外可积性条件下证明了 $L^1$ 解的存在唯一性，并利用随机 Gronwall 型和 Bihari 型不等式等创新技术扩展了已有结果。

临界二维随机热流、聚合物与GMC的矩比较不等式

Moments Comparison Inequalities for Critical 2d Stochastic Heat Flow, Polymers and GMC

本文利用高斯凸不等式和自举论证，为临界二维随机热流等对象建立了矩比较不等式，证明局部平均SHF的p阶矩与其二阶矩的p(p-1)/2次幂在乘法常数下互有界。