Tail asymptotics for monotone-separable networks

Moments and tails in monotone-separable stochastic networks

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework, which was first introduced to derive the stability region for stochastic networks with stationary and ergodic driving sequences, is revisited. It contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. Our purpose is the analysis of the tails of the stationary state variables in the particular c…

单调尾部函数：定义、性质及其在风险降低策略中的应用

Monotone tail functions: definitions, properties, and application to risk-reducing strategies

本文推广了单调尾部函数的理论，刻画了尾部变换下分位数的表达方式，并将其应用于期权定价、保险精算、象限完全相依分析及经济资本风险降低策略。

Monotone tail and moment ratio properties of Student's family of distributions

Let G_p denote the tail function of Student's distribution with p degrees of freedom. It is shown that the ratio G_q(x)/G_p(x) is decreasing in x>0 for any p and q such that 0<p<q\le\infty. Therefore, G_q(x)<G_p(x) for all such p and q and all x>0. Corollaries on the monotonicity of (generalized) moments and ratios thereof are also given.

Hilbert 空间中的单调保测映射：存在性、唯一性与稳定性

Monotone Measure-Preserving Maps in Hilbert Spaces: Existence, Uniqueness, and Stability

本文将 McCann 关于单调保测映射存在性与唯一性的结果推广至可分 Hilbert 空间，证明了在无矩假设下凸函数梯度的前推映射存在性及有界支撑下的唯一性，并建立了传输映射的稳定性，由此导出最优二次传输成本波动的中心极限定理。

Fluctuation theory for Lévy processes with completely monotone jumps

We study the Wiener-Hopf factorization for Lévy processes $X_t$ with completely monotone jumps. Extending previous results of L.C.G. Rogers, we prove that the space-time Wiener-Hopf factors are complete Bernstein functions of both the spatial and the temporal variable. As a corollary, we prove complete monotonicity of: (a) the tail of the distribution function of the supremum of $X_t$ up to an independent exponential time; (b) the Laplace transform of the supremum of $X_t$ up to a fixed time $T$, as a function of $T$. The proof involves a detailed analysis of the holomorphic extension of the c…

强定律、随机单调向量场以及非正曲率度量空间上的梯度流

Strong laws, random monotone vector fields and gradient flows on metric spaces of nonpositive curvature

本文在Hadamard空间上推广了Sturm强大数定律，建立了随机单调向量场的强定律，并由此推导出积分函数梯度流的概率Lie-Trotter-Kato公式，同时首次给出次微分与积分可交换性的非线性版本。