RELATIVE ENTROPY AND LARGE DEVIATIONS UNDER SUBLINEAR EXPECTATIONS

We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.

THE TRANSMISSION CAPACITY OF MANET BASED ON CONFLICT GRAPH

The transmission capacity of Mobile Ad Hoc Networking (MANET) is constrained by the mutual interference of concurrent transmissions between nodes. First, the transmission capacity of MANET is studied by the view of information flow between nodes. At the same time, the problem that the interference between nodes affects the transmission capacity of MANET is also studied by the tool of the event conflict graph. Secondly, the paper presents the method to compute the maximum ex- pectant achievable capacity for the given conflict graph, and concludes and proves an sufficient con- dition that the information flow transmit successfully between nodes. At last, the results are simulated and a fitting equation of transmission capacity between nodes is given.

The minimal sublinear expectations and their related properties

In this paper, we prove that for a sublinear expectation ?[·] defined on L 2(Ω, $ \mathcal{F} $ ), the following statements are equivalent: ? is a minimal member of the set of all sublinear expectations defined on L 2(Ω, $ \mathcal{F} $ )? is linearthe two-dimensional Jensen’s inequality for ? holds.Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation.

Multi-dimensional Central Limit Theorems and Laws of Large Numbers under Sublinear Expectations

In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.

Moment bounds for IID sequences under sublinear expectations

With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality,we get the following result:For any continuous functionsatisfying the growth condition |(x) | C(1 + |x|p) for some C > 0,p 1 depending on ,the central limit theorem under sublinear expectations obtained by Peng still holds.

Strong Laws of Large Numbers for Sublinear Expectation under Controlled 1st Moment Condition

This paper deals with strong laws of large numbers for sublinear expectation under controlled 1st moment condition. For a sequence of independent random variables,the author obtains a strong law of large numbers under conditions that there is a control random variable whose 1st moment for sublinear expectation is finite. By discussing the relation between sublinear expectation and Choquet expectation, for a sequence of i.i.d random variables, the author illustrates that only the finiteness of uniform 1st moment for sublinear expectation cannot ensure the validity of the strong law of large numbers which in turn reveals that our result does make sense.

Some Inequalities and Limit Theorems Under Sublinear Expectations

In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob＇s inequality for submartingale and Kolmogrov＇s inequality. By Kolmogrov＇s inequality, we obtain a special version of Kolmogrov＇s law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition.

Convergence rate of Peng’s law of large numbers under sublinear expectations

This short note provides a new and simple proof of the convergence rate for the Peng’s law of large numbers under sublinear expectations,which improves the results presented by Song[15]and Fang et al.[3].

G-Lévy processes under sublinear expectations

We introduce G-Lévy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations.We then obtain the Lévy-Khintchine formula and the existence for G-Lévy processes.We also introduce G-Poisson processes.

On the laws of the iterated logarithm with mean-uncertainty under sublinear expectations

A new Hartman-Wintner-type law of the iterated logarithm for independent random variables with mean-uncertainty under sublinear expectations is established by the martingale analogue of the Kolmogorov law of the iterated logarithm in classical probability theory.

Local Lipschitz-α Mappings and Applications to Sublinear Expectations

The aim of this paper is to establish a series of important properties of local Lipschitz-α mappings from a subset of a normed space into a normed space. These mappings include Lipschitz operators, Lipschitz-α operators and local Lipschitz functions. Some applications to the theory of sublinear expectation spaces are given.

A strong law of large numbers under sublinear expectations

We consider a sequence of independent and identically distributed(i.i.d.)random variables{ξ_(k)}under a sublinear expectation E=sup_(P∈Θ).We first give a new proof to the fact that,under each P∈Θ,any cluster point of the empirical averages.Next,we consider sublinear expectations on a Polish space,and show that for each constantμ∈[μ,μ^(-)],there exists a probability P_(μ)∈Θsuch thatlim_(n→∞)ξ_(n)=μ,P_(μ-a.s.,(0.1))supposing thatΘis weakly compact and.Under the same conditions,we obtain a generalization of(0.1)in the product space with replaced by.Here is a Borel measurable function on,.Finally,we characterize the triviality of the tail-algebra of the i.i.d.random variables under a sublinear expectation.

A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation

This article establishes a universal robust limit theorem under a sublinear expectation framework.Under moment and consistency conditions,we show that,forα∈(1,2),the i.i.d.sequence{(1/√∑_(i=1)^(n)X_(i),1/n∑_(i=1)^(n)X_(i)Y_(i),1/α√n∑_(i=1)^(n)X_(i))}_(n=1)^(∞)converges in distribution to L_(1),where L_(t=(ε_(t),η_(t),ζ_(t))),t∈[0,1],is a multidimensional nonlinear Lévy process with an uncertainty■set as a set of Lévy triplets.This nonlinear Lévy process is characterized by a fully nonlinear and possibly degenerate partial integro-differential equation(PIDE){δ_(t)u(t,x,y,z)-sup_(F_(μ),q,Q)∈■{∫_(R^(d)δλu(t,x,y,z)(dλ)with.To construct the limit process,we develop a novel weak convergence approach based on the notions of tightness and weak compactness on a sublinear expectation space.We further prove a new type of Lévy-Khintchine representation formula to characterize.As a byproduct,we also provide a probabilistic approach to prove the existence of the above fully nonlinear degenerate PIDE.

A general central limit theorem under sublinear expectations

Under some weaker conditions,we give a central limit theorem under sublinear expectations,which extends Peng's central limit theorem.

Convergences of Random Variables Under Sublinear Expectations

In this note, the authors survey the existing convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity property, the authors prove that convergence in capacity is stronger than convergence in distribution,and give some equivalent characterizations of convergence in distribution. In addition,they give a dominated convergence theorem under sublinear expectations, which may have its own interest.

STRONG LIMIT THEOREMS FOR EXTENDED INDEPENDENT RANDOM VARIABLES AND EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have attracted a lot of interest recently.The purpose of this paper is to study the strong law of large numbers and the law of the iterated logarithm for a sequence of random variables in a sub-linear expectation space under a concept of extended independence which is much weaker and easier to verify than the independence proposed by Peng[20].We introduce a concept of extended negative dependence which is an extension of the kind of weak independence and the extended negative independence relative to classical probability that has appeared in the recent literature.Powerful tools such as moment inequality and Kolmogorov’s exponential inequality are established for these kinds of extended negatively independent random variables,and these tools improve a lot upon those of Chen,Chen and Ng[1].The strong law of large numbers and the law of iterated logarithm are also obtained by applying these inequalities.

基于最优动态功率补偿的先进绝热压缩空气储能一次调频控制策略

随着大规模新能源接入电网,新型电力系统“低惯量、弱支撑”特征凸显,电网频率调节资源日益稀缺,系统频率稳定问题愈发严峻。先进绝热压缩空气储能(advanced adiabatic compressed air energy storage,AA-CAES)具有容量大、寿命长等优势而受到广泛关注,但由于其储能和释能过程涉及气-热动态耦合过程,调频特性较为复杂,调频潜力还有待挖掘。因此,首先建立AA-CAES系统全工况动态仿真模型,进而基于期望频率动态曲线设计AA-CAES系统调频传递函数,优化目标传递函数关键参数,实现AA-CAES最小动态功率补偿下满足系统频率调节需求。最后通过仿真实验,验证了所提控制策略可优化AA-CAES调频容量的同时减小系统的稳态频率偏差与频率超调量,显著改善频率响应特性,为建设电网友好型AA-CAES电站提供技术支撑。

次线性期望下独立同分布随机变量序列的完全收敛

概率空间下,随机变量和的期望等于随机变量期望的和,而在次线性期望空间,随机变量和的期望不再等于随机变量期望的和,经典概率空间中的结果无法直接运用于次线性期望空间。通过研究次线性期望空间下独立同分布(i.i.d.)的随机变量{X,X_(n),n≥1},在满足0<a_(n)/n↑以及0<a_(n)/n↑∞条件下随机变量序列的完全收敛关系,其中{a_(n),n≥1}是一个正的单调递增序列,文中将概率空间下的结果推广到次线性期望空间。

G-可料过程的Ito积分

可料过程是一种重要的随机过程.本文利用非线性随机分析理论方法,提出了G-可料过程的定义,拟发展次线性期望框架下的可料过程及其相关随机积分,探究了G-可料过程关于G-布朗运动以及G-布朗运动二次变差的Ito积分,得到了与其相关的若干性质.

欧盟与乌克兰关系新叙事中的“哥本哈根标准”

持续的俄乌冲突将欧盟与乌克兰的关系推向新纪元。乌克兰在危机中走向入盟申请,在乌克兰还未“达标”时,再以惊人的速度从候选国资格到2023年12月14日启动入盟谈判。欧盟与乌克兰关系的演变经历了四个阶段,即第一阶段的初步接触与入盟标准的提出,第二阶段邻国关系的提升,第三阶段结盟关系的巩固与安全因素的淡入,第四阶段建立地缘政治联盟。欧盟基于理性选择,在乌克兰危机爆发后将地缘安全利益推向首位,尽管乌克兰还没有“达到”欧盟要求的改革“标准”,仍为其“开绿灯”。对地缘政治的追求,暴露了欧盟捍卫其“哥本哈根标准”能力的局限性。