Moments of q-Normal and conditional q-Normal distributions

Conditional Value at Risk and Partial Moments for the Metalog Distributions

The metalog distributions represent a convenient way to approach many practical applications. Their distinctive feature is simple closed-form expressions for quantile functions. This paper contributes to further development of the metalog distributions by deriving the closed-form expressions for the Conditional Value at Risk, a risk measure that is closely related to the tail conditional expectations. It also addressed the derivation of the first-order partial moments and shows that they are convex with respect to the vector of the metalog distribution parameters.

条件期望锐界估计的广义矩方法

A generalized moment approach to sharp bounds for conditional expectations

本文提出广义矩方法的改编版，利用锥对偶性获得条件期望的锐界，并建立基于矩的分布鲁棒优化框架，用于不确定性下的决策。

随机Lasota-Yorke映射中具有孔的函数相关性界及其在条件正态近似中的应用

Functional correlation bound for random Lasota--Yorke maps with holes and its applications to conditional normal approximations

本文研究了由Lasota-Yorke映射族生成的随机开放动力系统统计性质，通过扩展函数相关性界框架，建立了具有指数衰减的FCB，并应用于条件中心极限定理和条件函数中心极限定理的正态近似。

q-Meixner过程的条件矩

Conditional moments of q-Meixner processes

证明了具有线性条件期望和二次条件方差的随机过程是马氏的，并且它们的转移概率与推广Meixner多项式的三参数正交多项式族有关.这些过程的特殊情况是由Levy过程的非对易推广引起的。

具有多项式条件矩和连续路径修正的平稳马尔可夫随机过程

Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths

本文研究具有条件多项式矩的平稳马尔可夫随机过程，给出用边缘分布偏度和超额峰度表示的连续路径修正存在性判据，并涵盖 Ornstein-Uhlenbeck 过程、Gamma 过程等实例。

q-高斯过程的经典版本：条件矩与Bell不等式

Classical versions of q-Gaussian processes: conditional moments and Bell's inequality

该研究针对满足q-交换关系的经典q-高斯过程，证明其具备线性回归与二次条件方差特性，并将Bell协方差不等式的适用范围从q=-1拓展至整个-1<q<1区间。

Normal approximation for mixtures of normal distributions and the evolution of phenotypic traits

An explicit bound is given for the Kolmogorov distance between a mixture of normal distributions and a normal distribution with properly chosen parameter values. A random variable X has a mixture of normal distributions if its conditional distribution given some sigma-algebra is normal. The bound depends only on the first two moments of the first two conditional moments of X given this sigma-algebra. As an application, the Yule-Ornstein-Uhlenbeck model, used in the field of phylogenetic comparative methods, is considered. A bound is derived for the Kolmogorov distance between the distribution …

条件高阶矩风险度量：具有FGM传染的二阶渐近性

The conditional higher moment risk measure: second-order asymptotics with FGM contagion

研究FGM相依结构下条件高阶矩相干风险度量的二阶渐近展开，利用极值理论等推导展开式，相比一阶结果能更准确捕捉高阶行为和相依效应，经模拟和实证应用验证了二阶方法的优势。

Weak variable step-size schemes for stochastic differential equations based on controlling conditional moments

We address the weak numerical solution of stochastic differential equations driven by independent Brownian motions (SDEs for short). This paper develops a new methodology to design adaptive strategies for determining automatically the step-sizes of the numerical schemes that compute the mean values of smooth functions of the solutions of SDEs. First, we introduce a general method for constructing variable step-size weak schemes for SDEs, which is based on controlling the match between the first conditional moments of the increments of the numerical integrator and the ones corresponding to an a…