Spatial extreme values: variational techniques and stochastic integrals

通过条件变分自编码器建模时空极值

Modeling Spatio-temporal Extremes via Conditional Variational Autoencoders

本文提出一种基于条件变分自编码器的模型，用于建模时空极值，并通过实验展示其在现实场景中的应用价值。

基于变分自编码器的地球系统模型植物生产力极端事件检测

Variational Autoencoders-based Detection of Extremes in Plant Productivity in an Earth System Model

本研究将变分自编码器（VAE）应用于地球系统模拟的总初级生产力极端事件检测，对比传统奇异谱分析（SSA），验证其性能相当且具计算与非线性捕捉优势，同时发现2050-2080年负碳循环极端事件将增加。

Extreme values for iterated integrals of the logarithm of the Riemann zeta-function

In this paper, we give an approximate formula for the measure of extreme values for the logarithm of the Riemann zeta-function and its iterated integrals. The result recovers the unconditional best result for the $Ω$-result of $S_{1}(t)$ for the part of minus of Tsang.

积分判别式的Gaussian-like固定点性质和变分特性

Gaussian-like fixed point and variational properties of integral discriminants

本文研究了积分判别式的Gaussian-like固定点性质和变分特性，通过扩展高斯极值原理，提出了更高效的矩-SOS层次结构以近似分部函数和矩。

A variational representation for G-Brownian functionals

The purpose of this paper is to establish a variational representation \log \E [e^{f(B)}] = \sup_h \E [f(B + \int_0^{\cdot} d<B>_s h_s) - 1/2 \int_0^1 h_s \cdot (d<B>_s h_s)] for functionals of the d-dimensional G-Brownian motion B. Here \E is a sublinear expectation called G-expectation, f is any bounded function in the domain of \E mapping C([0,1];\R^d) to \R, the integrals are taken with respect to the quadratic variation of B, and the supremum runs over all h's for which these integrals are well-defined. As an application, we give another proof of the results obtained by Gao-Jiang (2010), …

Implicit max-stable extremal integrals

Recently, the notion of implicit extreme value distributions has been established, which is based on a given loss function $f \ge 0$. From an application point of view, one is rather interested in extreme loss events that occur relative to $f$ than in the corresponding extreme values itself. In this context, so-called $f$-implicit $α$-Fréchet max-stable distributions arise and have been used to construct independently scattered sup-measures that possess such margins. In this paper we solve an open problem in [7] by developing a stochastic integral of a deterministic function $g\ge 0$ with resp…